Factors of 21

How to find the factors of 21

Test every whole number from 1 up to the square root of 21 (√21 ≈ 4.583). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 21 ÷ 1 = 21 — so 1 and 21 are factors
• 21 ÷ 2 = 10.5 — not a whole number
• 21 ÷ 3 = 7 — so 3 and 7 are factors
• 21 ÷ 4 = 5.25 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 7 and 21.

Prime factorization of 21

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

The primes you divided by give 21 = 3 × 7. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 21

• 21 is a composite number.
• The sum of all its factors is 32; the sum of its proper factors (excluding 21) is 11, which makes it a deficient number (its proper factors add up to less than itself).
• 21 is not a perfect square, so its factors pair up evenly.
• Multiples of 21 include 42, 63, 84, 105 and so on.

Factors vs. multiples

Factors of 21 are the numbers that divide into it; multiples of 21 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.