Factors of 364

How to find the factors of 364

Test every whole number from 1 up to the square root of 364 (√364 ≈ 19.079). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 364 ÷ 1 = 364 — so 1 and 364 are factors
• 364 ÷ 2 = 182 — so 2 and 182 are factors
• 364 ÷ 3 = 121.333 — not a whole number
• 364 ÷ 4 = 91 — so 4 and 91 are factors
• 364 ÷ 5 = 72.8 — not a whole number
• 364 ÷ 6 = 60.667 — not a whole number
• 364 ÷ 7 = 52 — so 7 and 52 are factors
• 364 ÷ 8 = 45.5 — not a whole number
• 364 ÷ 9 = 40.444 — not a whole number
• 364 ÷ 10 = 36.4 — not a whole number
• 364 ÷ 11 = 33.091 — not a whole number
• 364 ÷ 12 = 30.333 — not a whole number
• 364 ÷ 13 = 28 — so 13 and 28 are factors
• 364 ÷ 14 = 26 — so 14 and 26 are factors
• 364 ÷ 15 = 24.267 — not a whole number
• 364 ÷ 16 = 22.75 — not a whole number
• 364 ÷ 17 = 21.412 — not a whole number
• 364 ÷ 18 = 20.222 — not a whole number
• 364 ÷ 19 = 19.158 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 and 364.

Prime factorization of 364

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

The primes you divided by give 364 = 2² × 7 × 13. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) = 12.

Properties of 364

• 364 is a composite number.
• The sum of all its factors is 784; the sum of its proper factors (excluding 364) is 420, which makes it a abundant number (its proper factors add up to more than itself).
• 364 is not a perfect square, so its factors pair up evenly.
• Multiples of 364 include 728, 1,092, 1,456, 1,820 and so on.

Factors vs. multiples

Factors of 364 are the numbers that divide into it; multiples of 364 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.