The number 72 is a composite number, which means it has multiple factors. Factors are the numbers that can evenly divide a given number without leaving a remainder.

The factors of 72 are:

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

Here’s a brief explanation of each factor:

1: Every number is divisible by 1.

2: The number 72 is divisible by 2 because it is an even number.

3: The sum of the digits in 72 is divisible by 3 (7 + 2 = 9), so 72 is divisible by 3.

4: The number 72 is divisible by 4 because it is divisible by 2 twice.

6: The number 72 is divisible by 6 because it is divisible by both 2 and 3.

8: The number 72 is divisible by 8 because it is divisible by 2 three times.

9: The sum of the digits in 72 is divisible by 9 (7 + 2 = 9), so 72 is divisible by 9.

12: The number 72 is divisible by 12 because it is divisible by both 2 and 3.

18: The number 72 is divisible by 18 because it is divisible by both 2 and 9.

24: The number 72 is divisible by 24 because it is divisible by both 2 and 12.

36: The number 72 is divisible by 36 because it is divisible by both 4 and 9.

72: Every number is divisible by itself.

These factors can be useful in various mathematical calculations, such as finding common divisors, simplifying fractions, or solving equations involving the number 72.

## Factors of definition 72

I apologize for any confusion. The term “factors of definition” is not clear. However, if you meant the factors of 72, as I mentioned in the previous response, the factors of 72 are:

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

These numbers are the factors of 72 because they can evenly divide 72 without leaving a remainder.

#### How many Factors of 72

To determine the number of factors of 72, we can count the total number of distinct factors that evenly divide 72.

The prime factorization of 72 is: 2^3 * 3^2.

To find the total number of factors, we add 1 to the exponent of each prime factor in the prime factorization and multiply them together.

For 72, we have:

Exponent of 2: 3 + 1 = 4

Exponent of 3: 2 + 1 = 3

The total number of factors of 72 is calculated as (4) * (3) = 12.

Therefore, there are 12 factors of 72.

#### Factor Pairs of 72

The factor pairs of 72 are the pairs of numbers that, when multiplied together, result in the number 72. Here are all the factor pairs of 72:

1 × 72 = 72

2 × 36 = 72

3 × 24 = 72

4 × 18 = 72

6 × 12 = 72

8 × 9 = 72

These are the six factor pairs of 72.

#### All Factors of 72 using Multiplication

To find all the factors of 72 using multiplication, you can start by listing all the numbers that divide 72 without leaving a remainder, including both the divisors and the quotients. Here are all the factors of 72:

1 × 72 = 72

2 × 36 = 72

3 × 24 = 72

4 × 18 = 72

6 × 12 = 72

8 × 9 = 72

So, the factors of 72 using multiplication are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.