How to find the factors of 64
Test every whole number from 1 up to the square root of 64 (√64 ≈ 8.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 64 ÷ 1 = 64 — so 1 and 64 are factors
- 64 ÷ 2 = 32 — so 2 and 32 are factors
- 64 ÷ 3 = 21.333 — not a whole number
- 64 ÷ 4 = 16 — so 4 and 16 are factors
- 64 ÷ 5 = 12.8 — not a whole number
- 64 ÷ 6 = 10.667 — not a whole number
- 64 ÷ 7 = 9.143 — not a whole number
- 64 ÷ 8 = 8 — so 8 and 8 are factors
Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 8, 16, 32 and 64.
Prime factorization of 64
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 64 = 2⁶. From the exponents you can also count the factors without listing them: (6 + 1) = 7.
Properties of 64
- 64 is a composite number.
- The sum of all its factors is 127; the sum of its proper factors (excluding 64) is 63, which makes it a deficient number (its proper factors add up to less than itself).
- 64 is a perfect square: 8 × 8. Perfect squares always have an odd number of factors.
- 64 is also a perfect cube: 4³.
- Multiples of 64 include 128, 192, 256, 320 and so on.
Factors vs. multiples
Factors of 64 are the numbers that divide into it; multiples of 64 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 64?
The factors of 64 are 1, 2, 4, 8, 16, 32 and 64. Each of these divides 64 with no remainder.
How many factors does 64 have?
64 has 7 positive factors, which form 4 factor pairs. Counting negative factors as well doubles that to 14.
What is the prime factorization of 64?
64 = 2⁶. Its distinct prime factors are 2.
Is 64 a prime number?
No. 64 is composite because it has 7 factors, more than the two a prime number has.