The number 64 is an interesting integer with several factors. Factors of a number are the numbers that divide evenly into it without leaving a remainder. Here are the factors of 64:

- 1 and 64: Every number is divisible by 1 and itself, so 1 and 64 are both factors of 64.
- 2: 64 is divisible by 2, which means it can be divided evenly into two equal parts, resulting in 32.
- 4: 64 is also divisible by 4. When divided by 4, it yields 16.
- 8: 64 is divisible by 8, and dividing it by 8 gives us 8.
- 16: 64 divided by 16 equals 4.

As we can see, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. These factors are essential when performing operations like multiplication, division, or factoring the number 64. Additionally, the factors of a number are used in various mathematical concepts, such as finding the greatest common divisor or simplifying fractions.

## How many Factors of 64

To determine the total number of factors for a given number, we can start by listing all the prime factors of that number.

For 64, the prime factorization is 2^6 since 64 can be expressed as 2 × 2 × 2 × 2 × 2 × 2.

To find the number of factors, we can use the exponent rule. In this case, we add 1 to each exponent and then multiply the results.

Exponents: 6 (from 2^6)

Exponent rule: (6 + 1) = 7

Therefore, there are 7 factors of 64. These factors are 1, 2, 4, 8, 16, 32, and 64.

#### Factor Pairs of 64

Factor pairs of 64 are the pairs of numbers that, when multiplied together, result in 64. Here are the factor pairs of 64:

1 × 64 = 64

2 × 32 = 64

4 × 16 = 64

8 × 8 = 64

Therefore, the factor pairs of 64 are (1, 64), (2, 32), (4, 16), and (8, 8).

#### All Factors of 64 using Multiplication

To find all the factors of 64 using multiplication, we can start with the number 1 and multiply it by increasing integers until we reach the square root of 64. Since factors come in pairs, we will generate all the factors by finding their corresponding pairs.

Starting with 1, we find the corresponding factor pairs:

1 × 64 = 64 (pair: 1 and 64)

2 × 32 = 64 (pair: 2 and 32)

4 × 16 = 64 (pair: 4 and 16)

8 × 8 = 64 (pair: 8 and 8)

As we have reached the square root of 64, which is 8, we have considered all possible factor pairs. The factors of 64 are:

1, 2, 4, 8, 16, 32, and 64.