Factors of 338

How to find the factors of 338

Test every whole number from 1 up to the square root of 338 (√338 ≈ 18.385). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 338 ÷ 1 = 338 — so 1 and 338 are factors
• 338 ÷ 2 = 169 — so 2 and 169 are factors
• 338 ÷ 3 = 112.667 — not a whole number
• 338 ÷ 4 = 84.5 — not a whole number
• 338 ÷ 5 = 67.6 — not a whole number
• 338 ÷ 6 = 56.333 — not a whole number
• 338 ÷ 7 = 48.286 — not a whole number
• 338 ÷ 8 = 42.25 — not a whole number
• 338 ÷ 9 = 37.556 — not a whole number
• 338 ÷ 10 = 33.8 — not a whole number
• 338 ÷ 11 = 30.727 — not a whole number
• 338 ÷ 12 = 28.167 — not a whole number
• 338 ÷ 13 = 26 — so 13 and 26 are factors
• 338 ÷ 14 = 24.143 — not a whole number
• 338 ÷ 15 = 22.533 — not a whole number
• 338 ÷ 16 = 21.125 — not a whole number
• 338 ÷ 17 = 19.882 — not a whole number
• 338 ÷ 18 = 18.778 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 13, 26, 169 and 338.

Prime factorization of 338

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

The primes you divided by give 338 = 2 × 13². From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) = 6.

Properties of 338

• 338 is a composite number.
• The sum of all its factors is 549; the sum of its proper factors (excluding 338) is 211, which makes it a deficient number (its proper factors add up to less than itself).
• 338 is not a perfect square, so its factors pair up evenly.
• Multiples of 338 include 676, 1,014, 1,352, 1,690 and so on.

Factors vs. multiples

Factors of 338 are the numbers that divide into it; multiples of 338 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.