Factors of 200

How to find the factors of 200

Test every whole number from 1 up to the square root of 200 (√200 ≈ 14.142). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 200 ÷ 1 = 200 — so 1 and 200 are factors
• 200 ÷ 2 = 100 — so 2 and 100 are factors
• 200 ÷ 3 = 66.667 — not a whole number
• 200 ÷ 4 = 50 — so 4 and 50 are factors
• 200 ÷ 5 = 40 — so 5 and 40 are factors
• 200 ÷ 6 = 33.333 — not a whole number
• 200 ÷ 7 = 28.571 — not a whole number
• 200 ÷ 8 = 25 — so 8 and 25 are factors
• 200 ÷ 9 = 22.222 — not a whole number
• 200 ÷ 10 = 20 — so 10 and 20 are factors
• 200 ÷ 11 = 18.182 — not a whole number
• 200 ÷ 12 = 16.667 — not a whole number
• 200 ÷ 13 = 15.385 — not a whole number
• 200 ÷ 14 = 14.286 — 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 and 200.

Prime factorization of 200

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

The primes you divided by give 200 = 2³ × 5². From the exponents you can also count the factors without listing them: (3 + 1) × (2 + 1) = 12.

Properties of 200

• 200 is a composite number.
• The sum of all its factors is 465; the sum of its proper factors (excluding 200) is 265, which makes it a abundant number (its proper factors add up to more than itself).
• 200 is not a perfect square, so its factors pair up evenly.
• Multiples of 200 include 400, 600, 800, 1,000 and so on.

Factors vs. multiples

Factors of 200 are the numbers that divide into it; multiples of 200 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.