Factors of 784

How to find the factors of 784

Test every whole number from 1 up to the square root of 784 (√784 ≈ 28.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 784 ÷ 1 = 784 — so 1 and 784 are factors
• 784 ÷ 2 = 392 — so 2 and 392 are factors
• 784 ÷ 3 = 261.333 — not a whole number
• 784 ÷ 4 = 196 — so 4 and 196 are factors
• 784 ÷ 5 = 156.8 — not a whole number
• 784 ÷ 6 = 130.667 — not a whole number
• 784 ÷ 7 = 112 — so 7 and 112 are factors
• 784 ÷ 8 = 98 — so 8 and 98 are factors
• 784 ÷ 9 = 87.111 — not a whole number
• 784 ÷ 10 = 78.4 — not a whole number
• 784 ÷ 11 = 71.273 — not a whole number
• 784 ÷ 12 = 65.333 — not a whole number
• 784 ÷ 13 = 60.308 — not a whole number
• 784 ÷ 14 = 56 — so 14 and 56 are factors
• 784 ÷ 15 = 52.267 — not a whole number
• 784 ÷ 16 = 49 — so 16 and 49 are factors
• 784 ÷ 17 = 46.118 — not a whole number
• 784 ÷ 18 = 43.556 — not a whole number
• 784 ÷ 19 = 41.263 — not a whole number
• 784 ÷ 20 = 39.2 — not a whole number
• 784 ÷ 21 = 37.333 — not a whole number
• 784 ÷ 22 = 35.636 — not a whole number
• 784 ÷ 23 = 34.087 — not a whole number
• 784 ÷ 24 = 32.667 — not a whole number
• 784 ÷ 25 = 31.36 — not a whole number
• 784 ÷ 26 = 30.154 — not a whole number
• 784 ÷ 27 = 29.037 — not a whole number
• 784 ÷ 28 = 28 — so 28 and 28 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392 and 784.

Prime factorization of 784

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

The primes you divided by give 784 = 2⁴ × 7². From the exponents you can also count the factors without listing them: (4 + 1) × (2 + 1) = 15.

Properties of 784

• 784 is a composite number.
• The sum of all its factors is 1,767; the sum of its proper factors (excluding 784) is 983, which makes it a abundant number (its proper factors add up to more than itself).
• 784 is a perfect square: 28 × 28. Perfect squares always have an odd number of factors.
• Multiples of 784 include 1,568, 2,352, 3,136, 3,920 and so on.

Factors vs. multiples

Factors of 784 are the numbers that divide into it; multiples of 784 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.