How to find the factors of 72
Test every whole number from 1 up to the square root of 72 (√72 ≈ 8.485). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 72 ÷ 1 = 72 — so 1 and 72 are factors
- 72 ÷ 2 = 36 — so 2 and 36 are factors
- 72 ÷ 3 = 24 — so 3 and 24 are factors
- 72 ÷ 4 = 18 — so 4 and 18 are factors
- 72 ÷ 5 = 14.4 — not a whole number
- 72 ÷ 6 = 12 — so 6 and 12 are factors
- 72 ÷ 7 = 10.286 — not a whole number
- 72 ÷ 8 = 9 — so 8 and 9 are factors
Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Prime factorization of 72
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 72 = 2³ × 3². From the exponents you can also count the factors without listing them: (3 + 1) × (2 + 1) = 12.
Properties of 72
- 72 is a composite number.
- The sum of all its factors is 195; the sum of its proper factors (excluding 72) is 123, which makes it a abundant number (its proper factors add up to more than itself).
- 72 is not a perfect square, so its factors pair up evenly.
- Multiples of 72 include 144, 216, 288, 360 and so on.
Factors vs. multiples
Factors of 72 are the numbers that divide into it; multiples of 72 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.
Frequently asked questions
What are the factors of 72?
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. Each of these divides 72 with no remainder.
How many factors does 72 have?
72 has 12 positive factors, which form 6 factor pairs. Counting negative factors as well doubles that to 24.
What is the prime factorization of 72?
72 = 2³ × 3². Its distinct prime factors are 2 and 3.
Is 72 a prime number?
No. 72 is composite because it has 12 factors, more than the two a prime number has.