Calculators

Math

Factors

72 is highly composite with 12 factors, making it extremely versatile for division. It appears in geometry (pentagonal angles), finance (Rule of 72), and is the product of 8 × 9. 72 has 12 factors and is divisible by 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36. This high divisibility makes it useful in time calculations and geometric divisions.

All Factors

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

The prime factorization is: 72 = 2 x 2 x 2 x 3 x 3

Factoring of 72 Using Trial Division

Find the Factors of 72 :

• Calculate the square root of 72 which is 8.4853, and round it down to the closest whole number, 8, and use it in the next step.
• Test the integer values 1 through 8 for division into 72 where the remainder equals 0.
• We find 12 factors where the remainder of division is 0 and they are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Factor Pairs

1 × 72 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 × 12 = 72
8 × 9 = 72

The factor pairs (multiples) that equal 72 when multiplied together are: (1 and 72), (2 and 36), (3 and 24), (4 and 18), (6 and 12), (8 and 9), which we found by matching up all factors of 72 which are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Is 72 Prime or Composite?

72 is a composite number. Since it has more than two factors, we know that 72 is not prime, it is composite. Prime numbers only have two factors. They are evenly divisible by only 1 and itself.