Factors of 100

How to find the factors of 100

Test every whole number from 1 up to the square root of 100 (√100 ≈ 10.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 100 ÷ 1 = 100 — so 1 and 100 are factors
• 100 ÷ 2 = 50 — so 2 and 50 are factors
• 100 ÷ 3 = 33.333 — not a whole number
• 100 ÷ 4 = 25 — so 4 and 25 are factors
• 100 ÷ 5 = 20 — so 5 and 20 are factors
• 100 ÷ 6 = 16.667 — not a whole number
• 100 ÷ 7 = 14.286 — not a whole number
• 100 ÷ 8 = 12.5 — not a whole number
• 100 ÷ 9 = 11.111 — not a whole number
• 100 ÷ 10 = 10 — so 10 and 10 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 5, 10, 20, 25, 50 and 100.

Prime factorization of 100

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

The primes you divided by give 100 = 2² × 5². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) = 9.

Properties of 100

• 100 is a composite number.
• The sum of all its factors is 217; the sum of its proper factors (excluding 100) is 117, which makes it a abundant number (its proper factors add up to more than itself).
• 100 is a perfect square: 10 × 10. Perfect squares always have an odd number of factors.
• Multiples of 100 include 200, 300, 400, 500 and so on.

Factors vs. multiples

Factors of 100 are the numbers that divide into it; multiples of 100 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.