Factors Of 72

The factors of 72 are the numbers, which gives the result as 72 when multiplied together in pair of two. Factor pairs of the number 72 are the whole numbers which could be positive and negative but not a fraction or decimal number. For example, the factor pair of 13 is (1,13) and (-1,-13). When we multiply the pair of negative factors, the resulted number is the original number, such as multiplying -1 × -13, we get the number 13. Thus, we can consider both positive and negative factor pairs of 13. To find the factors of a number, 72, we will use the factorization method.

In this method, we consider first, 1 and 72 as factors of 72 and continue with finding the other pair of multiples of 72 which results in the original number. To understand in a better way, keep reading the article below to find the factors of 72 in pairs. Also, we will find here the prime factors of 72 with the help of the division method.

Pair Factors Of 72

We can find the pair factors of 72, by multiplying two numbers in a pair to get the original number as 72, such as;

If 1 × 72 = 72, then (1, 72) are pair factors of 72. Similarly, let us find other pair factors of 72.

2 × 36 = 72, (2, 36) are pair factors of 72

3 × 24 = 72, (3, 24) are pair factors of 72

4 × 18 = 72, (4, 18) are pair factors of 72

6 × 12 = 72, (6, 12) are pair factors of 72

Therefore, the positive pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18) and (6, 12).

Now if we have to find the negative pair factors of 72, then,

-1 × -72 = 72, then (-1, -72) are pair factors of 72

-2 × -36 = 72, (-2, -36) are pair factors of 72

-3 × -24 = 72, (-3, -24) are pair factors of 72

-4 × -18 = 72, (-4, -18) are pair factors of 72

-6 × -12 = 72, (-6, -12) are pair factors of 72

Therefore, the negative pair factors of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18) and (-6, -12).

How to find the factors of 72?

Let us learn the steps to find factors of 72.

  • First, write the number 72 in your notebook.
  • Find the two numbers, which on multiplication gives 72, say 3 and 24, such as 3 × 24 = 72.
  • We know 3 is a prime number which has only two factors, i.e., 1 and the number itself. So, we cannot further factorize it.
  • 3 = 3 × 1

  • But 24 is not a prime number but a composite number and can be further factorized.
  • 24 = 3 × 2 × 2 × 2 × 1

  • Therefore, the factorization of 72 gives us, 72 = 3 × 3 × 2 × 2 × 2 × 1
  • Write down all the unique numbers which we can obtain from 3 × 3 × 2 × 2 × 2 × 1.

Factors Of 72

1, 2, 3, 4, 6, 12, 18, 24, 36 and 24

Prime Factors of 72

The number 72 is a composite number. Now let us find the prime factors of 72.

  • The first step is to divide the number 72 with the smallest prime factor,i.e. 2.
  • 72 ÷ 2 = 36

    Again, divide 36 by 2.

    36 ÷ 2 = 18

    18 ÷ 2 = 9

    Now, if we divide 9 by 2 we get a fraction number, which cannot be a factor.

  • Now, proceed to the next prime numbers, i.e. 3.
  • 9 ÷ 3 = 3

    3 ÷ 3 = 1

  • We have received 1 at the end in the division process and further, we cannot proceed. So, the prime factors of 72 are 2 × 2 × 2 × 3 × 3 or 23 × 32, where 2 and 3 are the prime numbers.

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The figure can be formed in the shape of a die.

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