Factors of 72

Factors of 72 are numbers that divide 72 evenly, resulting in whole numbers without any remainder. Unlike prime numbers, which have only two factors (1 and the number itself), 72 is a composite number with multiple factors. When multiplying these factors in pairs, you get 72. Here are the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Also Check: Cube root table

Introduction

Factors of 72 can be both positive and negative, but they can't be fractions or decimals. For example, the factors can be (1, 72) or (-1, -72). When multiplying a pair of negative factors like -1 and -72, the result is still 72.

Factors of 72

Factors of 72 are numbers that divide it exactly without leaving a remainder. These factors can be paired to give the original number when multiplied. Since 72 is a composite number, it has more factors than just 1 and 72. Here are all the factors of 72:

Also Check: Differential Equations

Positive and Negative Factors of 72

Factors can be paired to produce 72. Here are the positive and negative pairs:

Prime Factorization of 72

Prime factorization breaks down a number into its basic building blocks, the prime numbers. Here’s how 72 can be factorized:

1. Divide 72 by the smallest prime number, which is 2: 72 ÷ 2 = 36
2. Divide 36 by 2: 36 ÷ 2 = 18
3. Divide 18 by 2: 18 ÷ 2 = 9
4. Divide 9 by the next smallest prime number, which is 3: 9 ÷ 3 = 3
5. Divide 3 by 3: 3 ÷ 3 = 1

So, the prime factorization of 72 is 2 × 2 × 2 × 3 × 3, or 2³×3²

Also Check: Discontinuity

Examples

1. Find the common factors of 72 and 73:

   • Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
   • Factors of 73: 1, 73 (since 73 is a prime number)

   The only common factor is 1.