Factors of 309

How to find the factors of 309

Test every whole number from 1 up to the square root of 309 (√309 ≈ 17.578). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 309 ÷ 1 = 309 — so 1 and 309 are factors
• 309 ÷ 2 = 154.5 — not a whole number
• 309 ÷ 3 = 103 — so 3 and 103 are factors
• 309 ÷ 4 = 77.25 — not a whole number
• 309 ÷ 5 = 61.8 — not a whole number
• 309 ÷ 6 = 51.5 — not a whole number
• 309 ÷ 7 = 44.143 — not a whole number
• 309 ÷ 8 = 38.625 — not a whole number
• 309 ÷ 9 = 34.333 — not a whole number
• 309 ÷ 10 = 30.9 — not a whole number
• 309 ÷ 11 = 28.091 — not a whole number
• 309 ÷ 12 = 25.75 — not a whole number
• 309 ÷ 13 = 23.769 — not a whole number
• 309 ÷ 14 = 22.071 — not a whole number
• 309 ÷ 15 = 20.6 — not a whole number
• 309 ÷ 16 = 19.313 — not a whole number
• 309 ÷ 17 = 18.176 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 103 and 309.

Prime factorization of 309

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

The primes you divided by give 309 = 3 × 103. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 309

• 309 is a composite number.
• The sum of all its factors is 416; the sum of its proper factors (excluding 309) is 107, which makes it a deficient number (its proper factors add up to less than itself).
• 309 is not a perfect square, so its factors pair up evenly.
• Multiples of 309 include 618, 927, 1,236, 1,545 and so on.

Factors vs. multiples

Factors of 309 are the numbers that divide into it; multiples of 309 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.