What number can divide in 54?

The integers that can divide 54 completely are known as its factors. By conducting prime factorization, we may discover the factors of 54. A number is divided into a group of prime numbers whose product produces the original number. This process is known as prime factorization or integer factorization.

In this article, we will learn about the factors of 54, how to find them by prime factorisation, common factors of 54 and factor pairs. We will also learn about the steps to find the factors of 54 with its factor tree of 54 and solved examples.

Read in detail about the Real Numbers here.

Factors of 54

A factor of a given number is an integer that divides the given number with no remainder. The factors of a composite number are many. A prime number, on the other hand, has only two factors, one and the number itself.

By examining the number’s divisibility, we can determine whether it is prime or composite. 54 is an even number as it can be divided by two. Thus, it is clear that 54 is a composite number made up of several factors.

Now, let’s find the factors of the number 54. Number 54 is divisible by 1, 2, 3, 6, 9, 18, 27 and 54. Hence, the numbers 1, 2, 3, 6, 9, 18, 27 and 54 are factors of the number 54.

Prime Factorization of 54

To perform the prime factorization of 54, we start to divide it by the smallest prime number which can completely divide 54. We know that it’s 2.

\(54 = 2\times27\)

\(54 = 2\times3\times9\)

\(54 = 2\times3\times3\times3\)

Thus, \(54 = 2\times3^3\)

We can also do this by upside-down method. So, now the prime factorization of 54 with the upside-down division method is \(2\times3\times3\times3/latex].

Check out this article on Even Numbers.

Common Factors of 54

If any of the factors are common for two or more numbers then they become the common factors of the two numbers. Every number will have common factors with one or another number. We have seen that the factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54.

Example: 

Factors of Number 54: 1, 2, 3, 6, 9, 18, 27 and 54.

Factors of Number 48: 1, 2, 3, 4, 6, 8, 12, 24, and 48.

Thus, 1, 2, 3 and 6 become the common factors of 54 and 48.

However, the number 2 is the lowest common factor.

Factor Pairs of 54

There are always two pairs of factors. When one number divides another, the resultant quotient also divides the original number. These quotients and divisors are referred to as factor pairs. There is a straightforward way for finding the factors of 54 in pairs; let’s try to understand it.

Now let’s see the factor tree of 54.

Learn the various concepts of Like Fractions here.

Steps to Find Factors of 54

Multiplication and division are the two ways of determining factors of 54. Furthermore, divisibility rules can be applied in both cases.

Factors By Multiplication

To find the factors using the multiplication follow the steps below:

Step 1: Use as many ways as you can to write the 54 as the product of two numbers. You will need to be quite familiar with tables to do this.

Step 2: The factors of 54 are all the numbers involved in these products.

Factors By Division

To find the factors using the division follow the steps below:

Step 1: Find every number that divides 54 less than or equal to 54. The smallest prime numbers should come first.

Step 2: Select out the numbers which can divide the given number using divisibility rules.

Step 3: Divide the number 54 by each of these numbers.

Step 4: The factors of the number are the divisors that do not result in any remainder.

Solved Example on Factors of 54

Now let’s see some solved examples on factors of 54.

Solved Example 1: Find the common factors of number 36 and number 54.

Solution: 

The factors of 36 are 1, 2, 3, 4, 9, 12, 36 and of 54 are 1, 2, 3, 6, 9, 18, 27 and 54.

Thus, the common factors are 1, 2, 3 and 4.

Solved Example 2: Rohan needs to split 54 apples among 6 people. Can it be divided evenly? How many apples each person will get?

Solution:

There are 54 apples and 6 people. Since 6 is a factor of 54, it completely divides 54. Thus, we can distribute the 54 apples evenly among six people.

Each person will get = 54/6 = 9 apples.

Solved Example 3: What is one-third of 54?

Solution:

One-third of 54 = \(54\times{1\over{3}}\).

One-third of 54 = \(18\)

Hope this article on the Factors of 54 was informative. Get some practice of the same on our free Testbook App. Download Now!

Factors of 54 FAQs

Ans.1 Multiples of 54 are numbers that have 54 as factors. The table of 54 are multiples of 54.

Ans.2 To perform the prime factorization of 54, we start to divide it by the smallest prime number which can completely divide 54. We know that it’s 2. \(54 = 2\times27\), \(54 = 2\times3\times9\), \(54 =2\times3\times3\times3\). Thus, \(54 = 2\times3^3\)

Ans.3 Composite numbers are numbers having factors other than the number itself and one. The factors of 32 are 1, 2, 4, 8, 16, and 32. Thus, 2 is the smallest factor of 32 after 1. 1, 2, 3, 6, 9, 18, 27 and 54 are factors of the number 54. Hence, by definition 54 is a composite number.

Ans.4 LCM or the least common multiple of any number with 54, is the smallest number that is common in the list of multiples of both numbers. For example, LCM of 54 and 72 is 216.

Ans.5 A factor is a number that divides a given integer by itself, leaving no residue.1, 2, 3, 6, 9, 18, 27 and 54 are factors of the number 54.

Okay, so when we ask if 54 is divisible by anything, we are looking to see if there are any WHOLE numbers that can be divided into 54 that will result in a whole number as the answer. In this short guide, we'll walk you through how to figure out whether 54 is divisible by anything. Let's go!

Fun fact! All whole numbers will have at least two numbers that they are divisible by. Those would be the actual number in question (in this case 54), and the number 1.

So, the answer is yes. The number 54 is divisible by 8 number(s).

Let's list out all of the divisors of 54:

When we list them out like this it's easy to see that the numbers which 54 is divisible by are 1, 2, 3, 6, 9, 18, 27, and 54.

You might be interested to know that all of the divisor numbers listed above are also known as the Factors of 54.

Not only that, but the numbers can also be called the divisors of 54. Basically, all of those numbers can go evenly into 54 with no remainder.

As you can see, this is a pretty simple one to calculate. All you need to do is list out all of the factors for the number 54. If there are any factors, then you know that 54 is divisible by something.

Give this a go for yourself and try to calculate a couple of these without using our calculator. Grab a pencil and a piece of paper and pick a couple of numbers to try it with.

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