Factors of 504

How to find the factors of 504

Test every whole number from 1 up to the square root of 504 (√504 ≈ 22.450). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 504 ÷ 1 = 504 — so 1 and 504 are factors
• 504 ÷ 2 = 252 — so 2 and 252 are factors
• 504 ÷ 3 = 168 — so 3 and 168 are factors
• 504 ÷ 4 = 126 — so 4 and 126 are factors
• 504 ÷ 5 = 100.8 — not a whole number
• 504 ÷ 6 = 84 — so 6 and 84 are factors
• 504 ÷ 7 = 72 — so 7 and 72 are factors
• 504 ÷ 8 = 63 — so 8 and 63 are factors
• 504 ÷ 9 = 56 — so 9 and 56 are factors
• 504 ÷ 10 = 50.4 — not a whole number
• 504 ÷ 11 = 45.818 — not a whole number
• 504 ÷ 12 = 42 — so 12 and 42 are factors
• 504 ÷ 13 = 38.769 — not a whole number
• 504 ÷ 14 = 36 — so 14 and 36 are factors
• 504 ÷ 15 = 33.6 — not a whole number
• 504 ÷ 16 = 31.5 — not a whole number
• 504 ÷ 17 = 29.647 — not a whole number
• 504 ÷ 18 = 28 — so 18 and 28 are factors
• 504 ÷ 19 = 26.526 — not a whole number
• 504 ÷ 20 = 25.2 — not a whole number
• 504 ÷ 21 = 24 — so 21 and 24 are factors
• 504 ÷ 22 = 22.909 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252 and 504.

Prime factorization of 504

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

The primes you divided by give 504 = 2³ × 3² × 7. From the exponents you can also count the factors without listing them: (3 + 1) × (2 + 1) × (1 + 1) = 24.

Properties of 504

• 504 is a composite number.
• The sum of all its factors is 1,560; the sum of its proper factors (excluding 504) is 1,056, which makes it a abundant number (its proper factors add up to more than itself).
• 504 is not a perfect square, so its factors pair up evenly.
• Multiples of 504 include 1,008, 1,512, 2,016, 2,520 and so on.

Factors vs. multiples

Factors of 504 are the numbers that divide into it; multiples of 504 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.