Factors of 782

How to find the factors of 782

Test every whole number from 1 up to the square root of 782 (√782 ≈ 27.964). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 782 ÷ 1 = 782 — so 1 and 782 are factors
• 782 ÷ 2 = 391 — so 2 and 391 are factors
• 782 ÷ 3 = 260.667 — not a whole number
• 782 ÷ 4 = 195.5 — not a whole number
• 782 ÷ 5 = 156.4 — not a whole number
• 782 ÷ 6 = 130.333 — not a whole number
• 782 ÷ 7 = 111.714 — not a whole number
• 782 ÷ 8 = 97.75 — not a whole number
• 782 ÷ 9 = 86.889 — not a whole number
• 782 ÷ 10 = 78.2 — not a whole number
• 782 ÷ 11 = 71.091 — not a whole number
• 782 ÷ 12 = 65.167 — not a whole number
• 782 ÷ 13 = 60.154 — not a whole number
• 782 ÷ 14 = 55.857 — not a whole number
• 782 ÷ 15 = 52.133 — not a whole number
• 782 ÷ 16 = 48.875 — not a whole number
• 782 ÷ 17 = 46 — so 17 and 46 are factors
• 782 ÷ 18 = 43.444 — not a whole number
• 782 ÷ 19 = 41.158 — not a whole number
• 782 ÷ 20 = 39.1 — not a whole number
• 782 ÷ 21 = 37.238 — not a whole number
• 782 ÷ 22 = 35.545 — not a whole number
• 782 ÷ 23 = 34 — so 23 and 34 are factors
• 782 ÷ 24 = 32.583 — not a whole number
• 782 ÷ 25 = 31.28 — not a whole number
• 782 ÷ 26 = 30.077 — not a whole number
• 782 ÷ 27 = 28.963 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 17, 23, 34, 46, 391 and 782.

Prime factorization of 782

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

The primes you divided by give 782 = 2 × 17 × 23. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 782

• 782 is a composite number.
• The sum of all its factors is 1,296; the sum of its proper factors (excluding 782) is 514, which makes it a deficient number (its proper factors add up to less than itself).
• 782 is not a perfect square, so its factors pair up evenly.
• Multiples of 782 include 1,564, 2,346, 3,128, 3,910 and so on.

Factors vs. multiples

Factors of 782 are the numbers that divide into it; multiples of 782 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.