The numbers that divide 54 completely, that is, without any remainder, are known as the factors of 54.

The factors of 54: 1, 2, 3, 6, 9, 18, 27 and 54.

So the fact here is that factors divide the number completely. As a result, they cannot be fractions or decimals. The method of prime factorization is applied to find the factors of 54.

54 is a composite number, as it has more than two factors. Hence, to factorize 54, we keep dividing 54 by its prime factors till we get 1 as the result. Let us look at how we can prime factorize 54:

54 ÷ 2 = 27

27 ÷ 3 = 9,

9 ÷ 3 = 3,

3 ÷ 3 = 1

Hence, the factor tree of 54 can be represented as a factor tree as shown in the image.

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When a pair of factors of 54 are multiplied together to get 54 as the result, they are said to be a factor pair of 54.

Hence, the positive pair factors are (1, 54), (2, 27), (3, 18) and (6, 9).

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

Solution:

The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 54: 1, 2, 3, 6, 9, 18, 27, 54.

So, the common factors of 36 and 54 are 1, 2, 3, 6, 9 and 18.

Hence, 54 and 36 have 6 common factors.

Example 2: There are 54 candies on a table. Tom is responsible for equally distributing the candies to six of his friends. What is the total number of candies that each of his friends will get after Tom distributes the candies?

Solution:

Total number of candies = 54

Total number of children = 6

The number of candies each friend gets = \(\frac{54}{6}\) = 9 R0

So, each of Tom’s friends will get 9 candies.

Example 3: Is 8 a factor of 54?

Solution:

No, 8 is not a factor of 54. As the number 8 does not divide 54 exactly. It leaves a remainder of 6. So, 8 is not a factor of 54.

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

So, the common factors of 18 and 54 are 1, 2, 3, 6, 9 and 18.

The prime factorization of 54 is 2 x 3 x 3 x 3. The prime factors of 54 are 2 and 3. As a result, the highest prime factor of 54 is 3.

Yes, 54 is a composite number as it has factors other than one and itself. It has the factors 2, 3, 6, 9, 18 and 27 other than 1 and 54.

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

So, the smallest factor of 54 is 1 and the greatest factor is 54 itself.

The following are some important properties of factors: