Factors of 252

How to find the factors of 252

Test every whole number from 1 up to the square root of 252 (√252 ≈ 15.875). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 252 ÷ 1 = 252 — so 1 and 252 are factors
• 252 ÷ 2 = 126 — so 2 and 126 are factors
• 252 ÷ 3 = 84 — so 3 and 84 are factors
• 252 ÷ 4 = 63 — so 4 and 63 are factors
• 252 ÷ 5 = 50.4 — not a whole number
• 252 ÷ 6 = 42 — so 6 and 42 are factors
• 252 ÷ 7 = 36 — so 7 and 36 are factors
• 252 ÷ 8 = 31.5 — not a whole number
• 252 ÷ 9 = 28 — so 9 and 28 are factors
• 252 ÷ 10 = 25.2 — not a whole number
• 252 ÷ 11 = 22.909 — not a whole number
• 252 ÷ 12 = 21 — so 12 and 21 are factors
• 252 ÷ 13 = 19.385 — not a whole number
• 252 ÷ 14 = 18 — so 14 and 18 are factors
• 252 ÷ 15 = 16.8 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126 and 252.

Prime factorization of 252

Divide by the smallest prime that fits, and keep going until the quotient is 1:

The primes you divided by give 252 = 2² × 3² × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) × (1 + 1) = 18.

Properties of 252

• 252 is a composite number.
• The sum of all its factors is 728; the sum of its proper factors (excluding 252) is 476, which makes it a abundant number (its proper factors add up to more than itself).
• 252 is not a perfect square, so its factors pair up evenly.
• Multiples of 252 include 504, 756, 1,008, 1,260 and so on.

Factors vs. multiples

Factors of 252 are the numbers that divide into it; multiples of 252 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.