Factors of 392

How to find the factors of 392

Test every whole number from 1 up to the square root of 392 (√392 ≈ 19.799). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 392 ÷ 1 = 392 — so 1 and 392 are factors
• 392 ÷ 2 = 196 — so 2 and 196 are factors
• 392 ÷ 3 = 130.667 — not a whole number
• 392 ÷ 4 = 98 — so 4 and 98 are factors
• 392 ÷ 5 = 78.4 — not a whole number
• 392 ÷ 6 = 65.333 — not a whole number
• 392 ÷ 7 = 56 — so 7 and 56 are factors
• 392 ÷ 8 = 49 — so 8 and 49 are factors
• 392 ÷ 9 = 43.556 — not a whole number
• 392 ÷ 10 = 39.2 — not a whole number
• 392 ÷ 11 = 35.636 — not a whole number
• 392 ÷ 12 = 32.667 — not a whole number
• 392 ÷ 13 = 30.154 — not a whole number
• 392 ÷ 14 = 28 — so 14 and 28 are factors
• 392 ÷ 15 = 26.133 — not a whole number
• 392 ÷ 16 = 24.5 — not a whole number
• 392 ÷ 17 = 23.059 — not a whole number
• 392 ÷ 18 = 21.778 — not a whole number
• 392 ÷ 19 = 20.632 — not a whole number

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

Prime factorization of 392

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

The primes you divided by give 392 = 2³ × 7². From the exponents you can also count the factors without listing them: (3 + 1) × (2 + 1) = 12.

Properties of 392

• 392 is a composite number.
• The sum of all its factors is 855; the sum of its proper factors (excluding 392) is 463, which makes it a abundant number (its proper factors add up to more than itself).
• 392 is not a perfect square, so its factors pair up evenly.
• Multiples of 392 include 784, 1,176, 1,568, 1,960 and so on.

Factors vs. multiples

Factors of 392 are the numbers that divide into it; multiples of 392 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.