Factors of 684

How to find the factors of 684

Test every whole number from 1 up to the square root of 684 (√684 ≈ 26.153). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 684 ÷ 1 = 684 — so 1 and 684 are factors
• 684 ÷ 2 = 342 — so 2 and 342 are factors
• 684 ÷ 3 = 228 — so 3 and 228 are factors
• 684 ÷ 4 = 171 — so 4 and 171 are factors
• 684 ÷ 5 = 136.8 — not a whole number
• 684 ÷ 6 = 114 — so 6 and 114 are factors
• 684 ÷ 7 = 97.714 — not a whole number
• 684 ÷ 8 = 85.5 — not a whole number
• 684 ÷ 9 = 76 — so 9 and 76 are factors
• 684 ÷ 10 = 68.4 — not a whole number
• 684 ÷ 11 = 62.182 — not a whole number
• 684 ÷ 12 = 57 — so 12 and 57 are factors
• 684 ÷ 13 = 52.615 — not a whole number
• 684 ÷ 14 = 48.857 — not a whole number
• 684 ÷ 15 = 45.6 — not a whole number
• 684 ÷ 16 = 42.75 — not a whole number
• 684 ÷ 17 = 40.235 — not a whole number
• 684 ÷ 18 = 38 — so 18 and 38 are factors
• 684 ÷ 19 = 36 — so 19 and 36 are factors
• 684 ÷ 20 = 34.2 — not a whole number
• 684 ÷ 21 = 32.571 — not a whole number
• 684 ÷ 22 = 31.091 — not a whole number
• 684 ÷ 23 = 29.739 — not a whole number
• 684 ÷ 24 = 28.5 — not a whole number
• 684 ÷ 25 = 27.36 — not a whole number
• 684 ÷ 26 = 26.308 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342 and 684.

Prime factorization of 684

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

The primes you divided by give 684 = 2² × 3² × 19. From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) × (1 + 1) = 18.

Properties of 684

• 684 is a composite number.
• The sum of all its factors is 1,820; the sum of its proper factors (excluding 684) is 1,136, which makes it a abundant number (its proper factors add up to more than itself).
• 684 is not a perfect square, so its factors pair up evenly.
• Multiples of 684 include 1,368, 2,052, 2,736, 3,420 and so on.

Factors vs. multiples

Factors of 684 are the numbers that divide into it; multiples of 684 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.