How to find the factors of 63
Test every whole number from 1 up to the square root of 63 (√63 ≈ 7.937). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 63 ÷ 1 = 63 — so 1 and 63 are factors
- 63 ÷ 2 = 31.5 — not a whole number
- 63 ÷ 3 = 21 — so 3 and 21 are factors
- 63 ÷ 4 = 15.75 — not a whole number
- 63 ÷ 5 = 12.6 — not a whole number
- 63 ÷ 6 = 10.5 — not a whole number
- 63 ÷ 7 = 9 — so 7 and 9 are factors
Collecting both numbers from every successful division gives the complete list: 1, 3, 7, 9, 21 and 63.
Prime factorization of 63
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 63 = 3² × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.
Properties of 63
- 63 is a composite number.
- The sum of all its factors is 104; the sum of its proper factors (excluding 63) is 41, which makes it a deficient number (its proper factors add up to less than itself).
- 63 is not a perfect square, so its factors pair up evenly.
- Multiples of 63 include 126, 189, 252, 315 and so on.
Factors vs. multiples
Factors of 63 are the numbers that divide into it; multiples of 63 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.
Frequently asked questions
What are the factors of 63?
The factors of 63 are 1, 3, 7, 9, 21 and 63. Each of these divides 63 with no remainder.
How many factors does 63 have?
63 has 6 positive factors, which form 3 factor pairs. Counting negative factors as well doubles that to 12.
What is the prime factorization of 63?
63 = 3² × 7. Its distinct prime factors are 3 and 7.
Is 63 a prime number?
No. 63 is composite because it has 6 factors, more than the two a prime number has.