Factors of 357

How to find the factors of 357

Test every whole number from 1 up to the square root of 357 (√357 ≈ 18.894). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 357 ÷ 1 = 357 — so 1 and 357 are factors
• 357 ÷ 2 = 178.5 — not a whole number
• 357 ÷ 3 = 119 — so 3 and 119 are factors
• 357 ÷ 4 = 89.25 — not a whole number
• 357 ÷ 5 = 71.4 — not a whole number
• 357 ÷ 6 = 59.5 — not a whole number
• 357 ÷ 7 = 51 — so 7 and 51 are factors
• 357 ÷ 8 = 44.625 — not a whole number
• 357 ÷ 9 = 39.667 — not a whole number
• 357 ÷ 10 = 35.7 — not a whole number
• 357 ÷ 11 = 32.455 — not a whole number
• 357 ÷ 12 = 29.75 — not a whole number
• 357 ÷ 13 = 27.462 — not a whole number
• 357 ÷ 14 = 25.5 — not a whole number
• 357 ÷ 15 = 23.8 — not a whole number
• 357 ÷ 16 = 22.313 — not a whole number
• 357 ÷ 17 = 21 — so 17 and 21 are factors
• 357 ÷ 18 = 19.833 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 7, 17, 21, 51, 119 and 357.

Prime factorization of 357

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

The primes you divided by give 357 = 3 × 7 × 17. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 357

• 357 is a composite number.
• The sum of all its factors is 576; the sum of its proper factors (excluding 357) is 219, which makes it a deficient number (its proper factors add up to less than itself).
• 357 is not a perfect square, so its factors pair up evenly.
• Multiples of 357 include 714, 1,071, 1,428, 1,785 and so on.

Factors vs. multiples

Factors of 357 are the numbers that divide into it; multiples of 357 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.