Factors of 756

How to find the factors of 756

Test every whole number from 1 up to the square root of 756 (√756 ≈ 27.495). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 756 ÷ 1 = 756 — so 1 and 756 are factors
• 756 ÷ 2 = 378 — so 2 and 378 are factors
• 756 ÷ 3 = 252 — so 3 and 252 are factors
• 756 ÷ 4 = 189 — so 4 and 189 are factors
• 756 ÷ 5 = 151.2 — not a whole number
• 756 ÷ 6 = 126 — so 6 and 126 are factors
• 756 ÷ 7 = 108 — so 7 and 108 are factors
• 756 ÷ 8 = 94.5 — not a whole number
• 756 ÷ 9 = 84 — so 9 and 84 are factors
• 756 ÷ 10 = 75.6 — not a whole number
• 756 ÷ 11 = 68.727 — not a whole number
• 756 ÷ 12 = 63 — so 12 and 63 are factors
• 756 ÷ 13 = 58.154 — not a whole number
• 756 ÷ 14 = 54 — so 14 and 54 are factors
• 756 ÷ 15 = 50.4 — not a whole number
• 756 ÷ 16 = 47.25 — not a whole number
• 756 ÷ 17 = 44.471 — not a whole number
• 756 ÷ 18 = 42 — so 18 and 42 are factors
• 756 ÷ 19 = 39.789 — not a whole number
• 756 ÷ 20 = 37.8 — not a whole number
• 756 ÷ 21 = 36 — so 21 and 36 are factors
• 756 ÷ 22 = 34.364 — not a whole number
• 756 ÷ 23 = 32.87 — not a whole number
• 756 ÷ 24 = 31.5 — not a whole number
• 756 ÷ 25 = 30.24 — not a whole number
• 756 ÷ 26 = 29.077 — not a whole number
• 756 ÷ 27 = 28 — so 27 and 28 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378 and 756.

Prime factorization of 756

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

The primes you divided by give 756 = 2² × 3³ × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (3 + 1) × (1 + 1) = 24.

Properties of 756

• 756 is a composite number.
• The sum of all its factors is 2,240; the sum of its proper factors (excluding 756) is 1,484, which makes it a abundant number (its proper factors add up to more than itself).
• 756 is not a perfect square, so its factors pair up evenly.
• Multiples of 756 include 1,512, 2,268, 3,024, 3,780 and so on.

Factors vs. multiples

Factors of 756 are the numbers that divide into it; multiples of 756 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.