The factors of 72 are the whole numbers that divide 72 exactly, leaving no remainder: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Use the calculator above for any number, or read on for the factor pairs, prime factorization and properties of 72.
What are the factors of 72?
A factor of 72 is any whole number that divides 72 with no remainder. Listing them from smallest to largest, the factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
So 72 is a composite number with 12 factors in total. Every number has 1 and itself as factors; the interesting work is finding the ones in between.
Factor pairs of 72
A factor pair is two numbers that multiply to give 72. The factor pairs of 72 are:
| Factor pair | Product |
|---|---|
| 1 × 72 | 72 |
| 2 × 36 | 72 |
| 3 × 24 | 72 |
| 4 × 18 | 72 |
| 6 × 12 | 72 |
| 8 × 9 | 72 |
Prime factorization of 72
The prime factorization breaks 72 down into a product of prime numbers only:
$$ 72 = 2^{3} \times 3^{2} $$How to find the factors of 72, step by step
- Start at 1 — 1 divides every number, so 1 and 72 are always factors.
- Test each whole number from 2 upward: if it divides 72 exactly, it is a factor.
- Use factor pairs — each small factor gives a matching large factor, so you only need to test up to $\sqrt{72}$.
- List them in order to get all 12 factors of 72.
Factors versus multiples of 72
It is easy to mix these up. The factors of 72 are the numbers that divide into 72 (they are less than or equal to 72), while the multiples of 72 are what you get by multiplying 72 outward: 72, 144, 216, 288, and so on. In short: factors go in, multiples go out. 72 is an even number, and its smallest prime factor is 2.
Properties of 72
| Number of factors | 12 |
| Sum of factors | 195 |
| Sum of proper divisors | 123 |
| Prime or composite | Composite |
| Even or odd | Even |
| Perfect square | No |
| Prime factorization | 2^3 x 3^2 |
Is 72 abundant, deficient or perfect?
Number theorists classify a number by comparing it to the sum of its proper divisors (all its factors except itself). For 72, those proper divisors add up to 123, which makes 72 an abundant number (its proper divisors sum to 123, which is more than 72). Most numbers are deficient; abundant and perfect numbers are comparatively rare, which is what makes this property interesting.
Using the factors of 72 for GCF and LCM
The prime factorization $2^{3} \times 3^{2}$ is the shortcut for combining 72 with another number. To find the greatest common factor (GCF), take the primes 72 shares with the other number, each to the lowest power. For the least common multiple (LCM), take every prime that appears in either number, each to the highest power. This is why the prime factorization is worth writing down — it does the heavy lifting for fractions, ratios and simplification.
Related factors and tools
Explore more: Factors of 70 Factors of 75 Factors of 66. Or find the factors of any number with the Factor Calculator. Exponents are the reverse idea — see logarithms and read the formal reference on divisors at Wikipedia.