Factors of 343

How to find the factors of 343

Test every whole number from 1 up to the square root of 343 (√343 ≈ 18.520). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 343 ÷ 1 = 343 — so 1 and 343 are factors
• 343 ÷ 2 = 171.5 — not a whole number
• 343 ÷ 3 = 114.333 — not a whole number
• 343 ÷ 4 = 85.75 — not a whole number
• 343 ÷ 5 = 68.6 — not a whole number
• 343 ÷ 6 = 57.167 — not a whole number
• 343 ÷ 7 = 49 — so 7 and 49 are factors
• 343 ÷ 8 = 42.875 — not a whole number
• 343 ÷ 9 = 38.111 — not a whole number
• 343 ÷ 10 = 34.3 — not a whole number
• 343 ÷ 11 = 31.182 — not a whole number
• 343 ÷ 12 = 28.583 — not a whole number
• 343 ÷ 13 = 26.385 — not a whole number
• 343 ÷ 14 = 24.5 — not a whole number
• 343 ÷ 15 = 22.867 — not a whole number
• 343 ÷ 16 = 21.438 — not a whole number
• 343 ÷ 17 = 20.176 — not a whole number
• 343 ÷ 18 = 19.056 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 7, 49 and 343.

Prime factorization of 343

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

The primes you divided by give 343 = 7³. From the exponents you can also count the factors without listing them: (3 + 1) = 4.

Properties of 343

• 343 is a composite number.
• The sum of all its factors is 400; the sum of its proper factors (excluding 343) is 57, which makes it a deficient number (its proper factors add up to less than itself).
• 343 is not a perfect square, so its factors pair up evenly.
• 343 is also a perfect cube: 7³.
• Multiples of 343 include 686, 1,029, 1,372, 1,715 and so on.

Factors vs. multiples

Factors of 343 are the numbers that divide into it; multiples of 343 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.