Factors of 840

How to find the factors of 840

Test every whole number from 1 up to the square root of 840 (√840 ≈ 28.983). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 840 ÷ 1 = 840 — so 1 and 840 are factors
• 840 ÷ 2 = 420 — so 2 and 420 are factors
• 840 ÷ 3 = 280 — so 3 and 280 are factors
• 840 ÷ 4 = 210 — so 4 and 210 are factors
• 840 ÷ 5 = 168 — so 5 and 168 are factors
• 840 ÷ 6 = 140 — so 6 and 140 are factors
• 840 ÷ 7 = 120 — so 7 and 120 are factors
• 840 ÷ 8 = 105 — so 8 and 105 are factors
• 840 ÷ 9 = 93.333 — not a whole number
• 840 ÷ 10 = 84 — so 10 and 84 are factors
• 840 ÷ 11 = 76.364 — not a whole number
• 840 ÷ 12 = 70 — so 12 and 70 are factors
• 840 ÷ 13 = 64.615 — not a whole number
• 840 ÷ 14 = 60 — so 14 and 60 are factors
• 840 ÷ 15 = 56 — so 15 and 56 are factors
• 840 ÷ 16 = 52.5 — not a whole number
• 840 ÷ 17 = 49.412 — not a whole number
• 840 ÷ 18 = 46.667 — not a whole number
• 840 ÷ 19 = 44.211 — not a whole number
• 840 ÷ 20 = 42 — so 20 and 42 are factors
• 840 ÷ 21 = 40 — so 21 and 40 are factors
• 840 ÷ 22 = 38.182 — not a whole number
• 840 ÷ 23 = 36.522 — not a whole number
• 840 ÷ 24 = 35 — so 24 and 35 are factors
• 840 ÷ 25 = 33.6 — not a whole number
• 840 ÷ 26 = 32.308 — not a whole number
• 840 ÷ 27 = 31.111 — not a whole number
• 840 ÷ 28 = 30 — so 28 and 30 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420 and 840.

Prime factorization of 840

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

The primes you divided by give 840 = 2³ × 3 × 5 × 7. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 32.

Properties of 840

• 840 is a composite number.
• The sum of all its factors is 2,880; the sum of its proper factors (excluding 840) is 2,040, which makes it a abundant number (its proper factors add up to more than itself).
• 840 is not a perfect square, so its factors pair up evenly.
• Multiples of 840 include 1,680, 2,520, 3,360, 4,200 and so on.

Factors vs. multiples

Factors of 840 are the numbers that divide into it; multiples of 840 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.