A number when divided by 115 leaves remainder 69 what is the remainder if a no is divided by 23

This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.

When you perform division, you can typically write down this operation in the following way:

where:

• a — Initial number you want to divide, called the dividend;
• n — Number you divide by; it is called the divisor;
• q — Result of division rounded down to the nearest integer; it is called the quotient; and
• r — Remainder of this mathematical operation.

When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise, the result will be correct in the terms of formulas, but will not make mathematical sense.

Make sure to check our modulo calculator for a practical application of the calculator with remainders.

🔎 If the remainder is zero, then we say that a is divisible by n. To learn more about this concept, check out Omni's divisibility test calculator.

1. Begin with writing down your problem. For example, you want to divide 346 by 7.
2. Decide on which of the numbers is the dividend, and which is the divisor. The dividend is the number that the operation is performed on – in this case, 346. The divisor is the number that actually "does the work" – in this case, 7.
3. Perform the division – you can use any calculator you want. You will get a result that most probably is not an integer – in this example, 49.4285714.
4. Round this number down. In our example, you will get 49.
5. Multiply the number you obtained in the previous step by the divisor. In our case, 49 * 7 = 343.
6. Subtract the number from the previous step from your dividend to get the remainder: 346 - 343 = 3.
7. You can always use our calculator with remainders instead and save yourself some time 😀

1. Make sure you have an unknown equal to two or more different modulos, e.g., x = d mod a, e mod b & f mod c.
2. Check that all modulos have the same greatest common divisor.
3. Multiply each modulo by all but one other modulo, until all combinations are found. For the above moduli, this would be: b*c, a*c, a*b.
4. Divide each number by the modulo that it is missing. If it equals the remainder for that modulo, e.g., (b*c)/a = d, leave the number as is.
5. If the remainder is not that for the modulo, use trial and error to find a positive integer to multiply the number by so that step 4 becomes true.
6. Add all numbers together once step 4 is true for all combinations.

It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.

Learning how to calculate the remainder has many real-world uses and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?

1. Set up your division, adding a decimal place followed by a zero after the dividend’s one’s column (if your dividend is already a decimal, add an additional zero to the end).
2. Perform the division as usual until you are left with the remainder.
3. Instead of writing the remainder after the quotient, move the remainder above the additional zero you placed.
4. If there is a remainder from this division, add another zero to the dividend and add the remainder to that.
5. Continue in this fashion until there is either: no remainder, the digit or digits repeat themselves endlessly, or you reach the desired degree of accuracy (3 decimal places is usually okay).
6. The result after the decimal place is the remainder as a decimal.

The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn’t entirely go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient, and 1 is the remainder.

Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!

There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.

The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case, it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.

The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

1. Subtract 7 from 24 repeatedly until the result is less than 7.
2. 24 minus 3 times 7 is 3.
3. The number that is left, 3, is the remainder.
4. This can be expressed as 3/7 in fractional form, or as 0.42857 in decimal form.

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Is the number 115 divisible by 69?

A natural number 'A' could only be divisible by another number 'B' if after dividing 'A' by 'B' the remainder was zero.

115 would be divisible by 69 only if there was a natural number 'n', so that:
115 = 'n' × 69

When we divide the two numbers, there is a remainder:

115 ÷ 69 = 1 + remainder 46

There is no natural number 'n' such that: 115 = 'n' × 69.

The number 115 is not divisible by 69.

1) If you subtract the remainder of the above operation from the original number, 115, then the result is a number that is divisible by the second number, 69:

115 - 46 = 69

69 = 1 × 69

2) If you subtract the remainder of the above operation from the second number, 69, and then add the result to the original number, 115, you get a number that is divisible by the second number:

69 - 46 = 23

115 + 23 = 138.

138 = 2 × 69.

The number 115 would be divisible by 69 only if its prime factorization contained all the prime factors that appear in the prime factorization of the number 69.

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

115 = 5 × 23
115 is not a prime number but a composite one.

69 = 3 × 23
69 is not a prime number but a composite one.

* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.

The prime factorization of the number 115 does not contain (all) the prime factors that occur in the prime factorization of 69.

The number 115 is not divisible by 69.

The number 115 is not divisible by 69. When the two numbers are divided, there is a remainder. The prime factorization of the number 115 does not contain (all) the prime factors that occur in the prime factorization of 69.

The divisibility of the natural numbers:

Method 1: Divide the numbers and check the remainder of the operation. If the remainder is zero, then the numbers are divisible.

Method 2: The prime factorization of the numbers (the decomposition of the numbers into prime factors).

• One natural number is said to be divisible by another natural number if after dividing the two numbers, the remainder of the operation is zero.
• Example: Let's divide two different numbers: 12 and 15, by 4.
• When dividing 12 by 4, the quotient is 3 and the remainder of the operation is zero.
• But when we divide 15 by 4, the quotient is 3 and the operation leaves a remainder of 3.
• We say that the number 12 is divisible by 4 and 15 is not divisible by 4.
• We also say that 4 is a divisor, or a factor, of 12, but not a factor (divisor) of 15.

• We say that the number "a" is divisible by "b", if there is an integer number "n", such that:
• a = n × b.
• The number "b" is called a divisor (or a factor) of "a" ("n" is also a divisor, or a factor, of "a").

• 0 is divisible by any number other than itself.
• 1 is a divisor (a factor) of every number.
• Improper factors: Any number "a", different of zero, is divisible at least by 1 and itself. In this case the number itself, "a", is called an improper factor (or an improper divisor). Some also consider 1 as an improper factor (divisor).
• Prime numbers: A number which is divisible only by 1 and itself is also called a prime number.
• Coprime numbers: If the greatest common factor of two numbers, "m" and "n", the GCF (m; n) = 1 - then it means that the two numbers are coprime, in other words they have no divisor other than 1. If a number "a" is divisible by these two coprime numbers, "m" and "n", then "a" is also divisible by their product, (m × n).
  • Example:
  • The number 84 is divisible by 4 and 3 and is also divisible by 4 × 3 = 12.
  • This is true because the two divisors, 3 and 4, are coprime.

• Calculating the divisors (factors) of a number is very useful when simplifying fractions (reducing fractions to lower terms).
• The established rules for finding factors (divisors) are based on the fact that the numbers are written in the decimal system:
• Multiples of 10 are divisible by 2 and 5, because 10 is divisible by 2 and 5
• Multiples of 100 are divisible by 4 and 25, because 100 is divisible by 4 and 25
• Multiples of 1,000 are divisible by 8, because 1,000 is divisible by 8.
• All the powers of 10, when divided by 3, or 9, have a remainder equal to 1.

• Due to the rules of operations with remainders, we have the following remainders when dividing numbers by 3 or 9:
• 600 leaves a remainder equal to 6 = 1 × 6 (1 for every 100)
• 240 = 2 × 100 + 4 × 10, then the remainder will be equal to 2 × 1 + 4 × 1 = 6

• When a number is divided by 3 or 9, the remainder is equal to what you get by dividing the sum of the digits of that number by 3 or 9:
• 7,309 has the sum of its digits: 7 + 3 + 0 + 9 = 19, which is divided with a remainder by either 3 or 9. So 7,309 is divisible by neither 3 nor by 9.

• All the even powers of 10, such as 102 = 100, 104 = 10,000, 106 = 1,000,000, and so on, when divided by 11 have a remainder equal to 1.
• All the odd powers of 10, such as 101 = 10, 103 = 1,000, 105 = 100,000, 107 = 10,000,000, and so on, when divided by 11 have a remainder equal to 10. In this case, the alternating sum of the digits of the number has the same remainder as the number itself when divided by 11.
• How is the alternating sum of the digits being calculated - it is shown in the example below.

• For instance, for the number: 85,976: 6 + 9 + 8 = 23, 7 + 5 = 12, the alternating sum of the digits: 23 - 12 = 11. So 85,976 is divisible by 11.

• 2, if the last digit is divisible by 2. If the last digit of a number is 0, 2, 4, 6 or 8, then the number is divisible by 2. For example, the number 20: 0 is divisible by 2, so then 20 must be divisible by 2 (indeed: 20 = 2 × 10).
• 3, if the sum of the digits of the number is divisible by 3. For example, the number 126: the sum of the digits is 1 + 2 + 6 = 9, which is divisible by 3. Then the number 126 must also be divisible by 3 (indeed: 126 = 3 × 42).
• 4, if the last two digits of the number make up a number that is divisible by 4. For example 124: 24 is divisible by 4 (24 = 4 × 6), so 124 is also divisible by 4 (indeed: 124 = 4 × 31).
• 5, if the last digit is divisible by 5 (the last digit is 0 or 5). For example 100: the last digit, 0, is divisible by 5, then the number 100 must be divisible by 5 (indeed: 100 = 5 × 20).
• 6, if the number is divisible by both 2 and 3. For example, the number 24 is divisible by 2 (24 = 2 × 12) and is also divisible by 3 (24 = 3 × 8), then it must be divisible by 6. Indeed, 24 = 6 × 4.
• 7, if the last digit of the number (the unit digit), doubled, subtracted from the number made up of the rest of the digits gives a number that is divisible by 7. The process can be repeated until a smaller number is obtained. For example, is the number 294 divisible by 7? We apply the algorithm: 29 - (2 × 4) = 29 - 8 = 21. 21 is divisible by 7. 21 = 7 × 3. But we could have applied the algorithm again, this time on the number 21: 2 - (2 × 1) = 2 - 2 = 0. Zero is divisible by 7, so 21 must be divisible by 7. If 21 is divisible by 7, then 294 must be divisible by 7.
• 8, if the last three digits of the number are making up a number that is divisible by 8. For example, the number 2,120: 120 is divisible by 8 since 120 = 8 × 15. Then 2,120 must also be divisible by 8. Proof: if we divide the numbers, 2,120 = 8 × 265.
• 9, if the sum of the digits of the number is divisible by 9. For example, the number 270 has the sum of the digits equal to 2 + 7 + 0 = 9, which is divisible by 9. Then 270 must also be divisible by 9. Indeed: 270 = 9 × 30.
• 10, if the last digit of the number is 0. Example, 140 is divisible by 10, since 140 = 10 × 14.
• 11 if the alternating sum of the digits is divisible by 11. For example, the number 2,915 has the alternating sum of the digits equal to: (5 + 9) - (1 + 2) = 14 - 3 = 11, which is divisible by 11. Then the number 2,915 must also be divisible by 11: 2,915 = 11 × 265.
• 25, if the last two digits of the number are making up a number that is divisible by 25. For example, the number made up by the last two digits of the number 275 is 75, which is divisible by 25, since 75 = 25 × 3. Then 275 must also be divisible by 25: 275 = 25 × 11.

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples