Factors of 351

How to find the factors of 351

Test every whole number from 1 up to the square root of 351 (√351 ≈ 18.735). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 351 ÷ 1 = 351 — so 1 and 351 are factors
• 351 ÷ 2 = 175.5 — not a whole number
• 351 ÷ 3 = 117 — so 3 and 117 are factors
• 351 ÷ 4 = 87.75 — not a whole number
• 351 ÷ 5 = 70.2 — not a whole number
• 351 ÷ 6 = 58.5 — not a whole number
• 351 ÷ 7 = 50.143 — not a whole number
• 351 ÷ 8 = 43.875 — not a whole number
• 351 ÷ 9 = 39 — so 9 and 39 are factors
• 351 ÷ 10 = 35.1 — not a whole number
• 351 ÷ 11 = 31.909 — not a whole number
• 351 ÷ 12 = 29.25 — not a whole number
• 351 ÷ 13 = 27 — so 13 and 27 are factors
• 351 ÷ 14 = 25.071 — not a whole number
• 351 ÷ 15 = 23.4 — not a whole number
• 351 ÷ 16 = 21.938 — not a whole number
• 351 ÷ 17 = 20.647 — not a whole number
• 351 ÷ 18 = 19.5 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 13, 27, 39, 117 and 351.

Prime factorization of 351

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

The primes you divided by give 351 = 3³ × 13. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) = 8.

Properties of 351

• 351 is a composite number.
• The sum of all its factors is 560; the sum of its proper factors (excluding 351) is 209, which makes it a deficient number (its proper factors add up to less than itself).
• 351 is not a perfect square, so its factors pair up evenly.
• Multiples of 351 include 702, 1,053, 1,404, 1,755 and so on.

Factors vs. multiples

Factors of 351 are the numbers that divide into it; multiples of 351 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.