Factors of 369

How to find the factors of 369

Test every whole number from 1 up to the square root of 369 (√369 ≈ 19.209). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 369 ÷ 1 = 369 — so 1 and 369 are factors
• 369 ÷ 2 = 184.5 — not a whole number
• 369 ÷ 3 = 123 — so 3 and 123 are factors
• 369 ÷ 4 = 92.25 — not a whole number
• 369 ÷ 5 = 73.8 — not a whole number
• 369 ÷ 6 = 61.5 — not a whole number
• 369 ÷ 7 = 52.714 — not a whole number
• 369 ÷ 8 = 46.125 — not a whole number
• 369 ÷ 9 = 41 — so 9 and 41 are factors
• 369 ÷ 10 = 36.9 — not a whole number
• 369 ÷ 11 = 33.545 — not a whole number
• 369 ÷ 12 = 30.75 — not a whole number
• 369 ÷ 13 = 28.385 — not a whole number
• 369 ÷ 14 = 26.357 — not a whole number
• 369 ÷ 15 = 24.6 — not a whole number
• 369 ÷ 16 = 23.063 — not a whole number
• 369 ÷ 17 = 21.706 — not a whole number
• 369 ÷ 18 = 20.5 — not a whole number
• 369 ÷ 19 = 19.421 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 41, 123 and 369.

Prime factorization of 369

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

The primes you divided by give 369 = 3² × 41. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.

Properties of 369

• 369 is a composite number.
• The sum of all its factors is 546; the sum of its proper factors (excluding 369) is 177, which makes it a deficient number (its proper factors add up to less than itself).
• 369 is not a perfect square, so its factors pair up evenly.
• Multiples of 369 include 738, 1,107, 1,476, 1,845 and so on.

Factors vs. multiples

Factors of 369 are the numbers that divide into it; multiples of 369 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.