Factors of 999

How to find the factors of 999

Test every whole number from 1 up to the square root of 999 (√999 ≈ 31.607). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 999 ÷ 1 = 999 — so 1 and 999 are factors
• 999 ÷ 2 = 499.5 — not a whole number
• 999 ÷ 3 = 333 — so 3 and 333 are factors
• 999 ÷ 4 = 249.75 — not a whole number
• 999 ÷ 5 = 199.8 — not a whole number
• 999 ÷ 6 = 166.5 — not a whole number
• 999 ÷ 7 = 142.714 — not a whole number
• 999 ÷ 8 = 124.875 — not a whole number
• 999 ÷ 9 = 111 — so 9 and 111 are factors
• 999 ÷ 10 = 99.9 — not a whole number
• 999 ÷ 11 = 90.818 — not a whole number
• 999 ÷ 12 = 83.25 — not a whole number
• 999 ÷ 13 = 76.846 — not a whole number
• 999 ÷ 14 = 71.357 — not a whole number
• 999 ÷ 15 = 66.6 — not a whole number
• 999 ÷ 16 = 62.438 — not a whole number
• 999 ÷ 17 = 58.765 — not a whole number
• 999 ÷ 18 = 55.5 — not a whole number
• 999 ÷ 19 = 52.579 — not a whole number
• 999 ÷ 20 = 49.95 — not a whole number
• 999 ÷ 21 = 47.571 — not a whole number
• 999 ÷ 22 = 45.409 — not a whole number
• 999 ÷ 23 = 43.435 — not a whole number
• 999 ÷ 24 = 41.625 — not a whole number
• 999 ÷ 25 = 39.96 — not a whole number
• 999 ÷ 26 = 38.423 — not a whole number
• 999 ÷ 27 = 37 — so 27 and 37 are factors
• 999 ÷ 28 = 35.679 — not a whole number
• 999 ÷ 29 = 34.448 — not a whole number
• 999 ÷ 30 = 33.3 — not a whole number
• 999 ÷ 31 = 32.226 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 27, 37, 111, 333 and 999.

Prime factorization of 999

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

The primes you divided by give 999 = 3³ × 37. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) = 8.

Properties of 999

• 999 is a composite number.
• The sum of all its factors is 1,520; the sum of its proper factors (excluding 999) is 521, which makes it a deficient number (its proper factors add up to less than itself).
• 999 is not a perfect square, so its factors pair up evenly.
• Multiples of 999 include 1,998, 2,997, 3,996, 4,995 and so on.

Factors vs. multiples

Factors of 999 are the numbers that divide into it; multiples of 999 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.