Factors of 1,000

How to find the factors of 1,000

Test every whole number from 1 up to the square root of 1,000 (√1,000 ≈ 31.623). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 1,000 ÷ 1 = 1,000 — so 1 and 1,000 are factors
• 1,000 ÷ 2 = 500 — so 2 and 500 are factors
• 1,000 ÷ 3 = 333.333 — not a whole number
• 1,000 ÷ 4 = 250 — so 4 and 250 are factors
• 1,000 ÷ 5 = 200 — so 5 and 200 are factors
• 1,000 ÷ 6 = 166.667 — not a whole number
• 1,000 ÷ 7 = 142.857 — not a whole number
• 1,000 ÷ 8 = 125 — so 8 and 125 are factors
• 1,000 ÷ 9 = 111.111 — not a whole number
• 1,000 ÷ 10 = 100 — so 10 and 100 are factors
• 1,000 ÷ 11 = 90.909 — not a whole number
• 1,000 ÷ 12 = 83.333 — not a whole number
• 1,000 ÷ 13 = 76.923 — not a whole number
• 1,000 ÷ 14 = 71.429 — not a whole number
• 1,000 ÷ 15 = 66.667 — not a whole number
• 1,000 ÷ 16 = 62.5 — not a whole number
• 1,000 ÷ 17 = 58.824 — not a whole number
• 1,000 ÷ 18 = 55.556 — not a whole number
• 1,000 ÷ 19 = 52.632 — not a whole number
• 1,000 ÷ 20 = 50 — so 20 and 50 are factors
• 1,000 ÷ 21 = 47.619 — not a whole number
• 1,000 ÷ 22 = 45.455 — not a whole number
• 1,000 ÷ 23 = 43.478 — not a whole number
• 1,000 ÷ 24 = 41.667 — not a whole number
• 1,000 ÷ 25 = 40 — so 25 and 40 are factors
• 1,000 ÷ 26 = 38.462 — not a whole number
• 1,000 ÷ 27 = 37.037 — not a whole number
• 1,000 ÷ 28 = 35.714 — not a whole number
• 1,000 ÷ 29 = 34.483 — not a whole number
• 1,000 ÷ 30 = 33.333 — not a whole number
• 1,000 ÷ 31 = 32.258 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 and 1,000.

Prime factorization of 1,000

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

The primes you divided by give 1,000 = 2³ × 5³. From the exponents you can also count the factors without listing them: (3 + 1) × (3 + 1) = 16.

Properties of 1,000

• 1,000 is a composite number.
• The sum of all its factors is 2,340; the sum of its proper factors (excluding 1,000) is 1,340, which makes it a abundant number (its proper factors add up to more than itself).
• 1,000 is not a perfect square, so its factors pair up evenly.
• 1,000 is also a perfect cube: 10³.
• Multiples of 1,000 include 2,000, 3,000, 4,000, 5,000 and so on.

Factors vs. multiples

Factors of 1,000 are the numbers that divide into it; multiples of 1,000 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.