# What Is The Prime Factorization Of 72

2 3 ⋅ 3 2

## Frequently Asked Questions on Factors of 72

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

## How To Calculate the Factors of 72?

To find the factors of 72, start dividing 72 by the smallest natural number that divides 72 perfectly and does not leave any remainder.

Continue dividing 72 by consecutive whole numbers, if the quotient is a whole number, it is a perfect divisor of 72. Hence, also it is a factor of 72.

If the quotient is a number in a fraction, it is not a factor of 72. Now let’s start the procedure:

Divide 72 by the smallest natural number i.e., 1.

As it has completely divided 72 without any leaving a remainder, so 1 is a factor of 72.

Now, divide 72 by the smallest even prime number i.e., 2

The number 72 has been divided perfectly by its divisor. So, the 2 is also a factor of 72.

Again divide 72 by the smallest odd prime number, which is 3

As 3 has divided 72 completely. So, the number 3, too is a factor of 72.

For getting more factors, divided 72 by natural numbers that exactly divide 72 and leave zero remainders as shown below:

All the above numbers completely divide 72 and do not leave any remainder. So, all these numbers are factors of 72.

The method stated above is called calculating the factors by division method. There are various methods to calculate the factors of 72. Other methods are also explained in this article.

## What are the Factors of 72?

The factors of 72 are the numbers that divide 72 exactly without leaving any remainder. In other words, the factors of 72 are the numbers that are multiplied in pairs resulting in an original number 72. As the number 72 is a composite number, it has many factors other than one and the number itself. Thus the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. Prime Factorization of 72: 2 × 2 × 2 × 3 × 3 or 23 × 32

The pair factors of 72 are the pair of numbers, which are multiplied together resulting in an original number 72. The pair factors of 72 can be positive pair or negative pair. If we multiply the pair of negative numbers, it will result in an original number 72. Thus, the positive and the negative pair factors of 72 are as follows:

Positive Pair Factors of 72:

 Positive Factors of 72 Positive Pair Factors of 72 1 × 72 (1, 72) 2 × 36 (2, 36) 3 × 24 (3, 24) 4 × 18 (4, 18) 6 × 12 (6, 12) 8 × 9 (8, 9)

Hence, the positive pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12) and (8, 9).

Negative Pair Factors of 72:

 Negative Factors of 72 Negative Pair Factors of 72 -1 × -72 (-1, -72) -2 × -36 (-2, -36) -3 × -24 (-3, -24) -4 × -18 (-4, -18) -6 × -12 (-6, -12) -8 × -9 (-8, -9)

Hence, the negative pair factors of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12) and (-8, -9).

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

• The first step is to divide the number 72 with the smallest prime factor,i.e. 2.
• 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.
• We have received 1 at the end of the division process and further, we cannot proceed. So, the prime factorisation of 72 is 2 × 2 × 2 × 3 × 3 or 23 × 32, where 2 and 3 are the prime numbers.
• Example 1:

Find the common factors of 72 and 71.

Solution:

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

The factors of 71 are 1 and 71.

Thus, the common factor of 72 and 71 is 1.

Example 2:

Find the common factors of 72 and 73.

Solution:

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Factors of 73 = 1 and 73.

As 73 is a prime number, the common factor of 72 and 73 is 1.

Example 3:

Find the common factors of 72 and 70.

Solution:

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

Therefore, the common factors of 70 and 72 are 1 and 2.

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