What are the factor pairs of 64?

The pairs are (1, 64), (2, 32), (4, 16) and (8, 8). Each pair multiplies to 64.

What is the greatest common factor of 64 and 96?

The GCF of 64 and 96 is 32. The common factors are 1, 2, 4, 8, 16 and 32, and 32 is the largest.

Factors of 64 - Factor Pairs & Prime Factorization

Q: What are the factors of 64?

The factors of 64 are 1, 2, 4, 8, 16, 32 and 64. That is seven factors, and each one divides 64 exactly.

Q: What is the prime factorization of 64?

64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶. Its only prime factor is 2.

What Are the Factors of 64?

A chessboard has 64 squares in 8 rows of 8, and 64 is also a power of 2. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.

The factors of 64 are 1, 2, 4, 8, 16, 32 and 64. That is seven factors.

Factor Pairs of 64

Look for pairs that multiply to 64, working from the outside in.

Handwritten notebook page titled Factors of 64 showing 1 × 64, 2 × 32, 4 × 16, 8 × 8 all equal to 64, with the seven factors 1, 2, 4, 8, 16, 32 and 64 circled in red and the note 7 factors — The 4 pairs of 64, with every factor circled.

Start with 1 × 64.
Try 2. Since 64 ÷ 2 = 32, write 2 × 32.
Try 4. Since 64 ÷ 4 = 16, write 4 × 16.
Try 8. Since 64 ÷ 8 = 8, write 8 × 8. The two numbers match, so you are done.

Prime Factorization of 64

Prime factors show what 64 is built from. Split it and keep going until every branch is a prime.

Handwritten factor tree of 64 splitting down to the circled primes 2, 2, 2, 2, 2 and 2, with 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶ written below — Factor tree of 64. The circled primes are 2, 2, 2, 2, 2 and 2.

So 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶. Its only prime factor is 2. Add 1 to each exponent and multiply: (6 + 1) = 7, which matches the list.

Divisibility check for 64

A number is a multiple of 64 when you can halve it 6 times in a row with no remainder. Take 192: halving gives 96, 48, 24, 12, 6 and 3, which is six halvings with no remainder, so 192 is a multiple of 64.

Is 64 a Prime or Composite Number?

Composite. It has seven factors. The sum of all factors is 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127. The factors smaller than 64 add up to 63, which is less than 64, so 64 is called a deficient number. 7 is an odd number of factors, because 8 is paired with itself.

Real-Life Uses of the Factors of 64

Chess. A chessboard has 64 squares in 8 rows of 8.
Computers. Because 64 = 2⁶, it shows up in memory sizes and 64-bit processors.
Halving. You can halve 64 six times in a row and stay with whole numbers.

Common Factors of 64 With Other Numbers

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96, so 64 and 96 share 1, 2, 4, 8, 16 and 32. The GCF is 32, which simplifies 64/96 to 2/3.

Quick Practice

Which of these are factors of 64: 5, 8 or 7? Only 8. Now try 70 and check it with the calculator.

Factors of 64