Factors of 345

How to find the factors of 345

Test every whole number from 1 up to the square root of 345 (√345 ≈ 18.574). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 345 ÷ 1 = 345 — so 1 and 345 are factors
• 345 ÷ 2 = 172.5 — not a whole number
• 345 ÷ 3 = 115 — so 3 and 115 are factors
• 345 ÷ 4 = 86.25 — not a whole number
• 345 ÷ 5 = 69 — so 5 and 69 are factors
• 345 ÷ 6 = 57.5 — not a whole number
• 345 ÷ 7 = 49.286 — not a whole number
• 345 ÷ 8 = 43.125 — not a whole number
• 345 ÷ 9 = 38.333 — not a whole number
• 345 ÷ 10 = 34.5 — not a whole number
• 345 ÷ 11 = 31.364 — not a whole number
• 345 ÷ 12 = 28.75 — not a whole number
• 345 ÷ 13 = 26.538 — not a whole number
• 345 ÷ 14 = 24.643 — not a whole number
• 345 ÷ 15 = 23 — so 15 and 23 are factors
• 345 ÷ 16 = 21.563 — not a whole number
• 345 ÷ 17 = 20.294 — not a whole number
• 345 ÷ 18 = 19.167 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 5, 15, 23, 69, 115 and 345.

Prime factorization of 345

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

The primes you divided by give 345 = 3 × 5 × 23. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 345

• 345 is a composite number.
• The sum of all its factors is 576; the sum of its proper factors (excluding 345) is 231, which makes it a deficient number (its proper factors add up to less than itself).
• 345 is not a perfect square, so its factors pair up evenly.
• Multiples of 345 include 690, 1,035, 1,380, 1,725 and so on.

Factors vs. multiples

Factors of 345 are the numbers that divide into it; multiples of 345 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.