# Factors of 64

Factors of 64 are 1, 2, 4, 8, 16, 32, and 64

#### How to find factors of a number

 1.   Find factors of 64 using Division Method 2.   Find factors of 64 using Prime Factorization 3.   Find factors of 64 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 64

• Divide 64 by 1: 64 ÷ 1 : Remainder = 0
• Divide 64 by 2: 64 ÷ 2 : Remainder = 0
• Divide 64 by 4: 64 ÷ 4 : Remainder = 0
• Divide 64 by 8: 64 ÷ 8 : Remainder = 0
• Divide 64 by 16: 64 ÷ 16 : Remainder = 0
• Divide 64 by 32: 64 ÷ 32 : Remainder = 0
• Divide 64 by 64: 64 ÷ 64 : Remainder = 0

Hence, Factors of 64 are 1, 2, 4, 8, 16, 32, and 64

#### 2. Steps to find factors of 64 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 64 using the division method, follow these steps:

• Step 1. Start dividing 64 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 64, which is 2. Divide 64 by 2 to obtain the quotient (32).
64 ÷ 2 = 32
• Step 3. Repeat step 1 with the obtained quotient (32).
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So, the prime factorization of 64 is, 64 = 2 x 2 x 2 x 2 x 2 x 2.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 64 as shown below:

So, the prime factorization of 64 is, 64 = 2 x 2 x 2 x 2 x 2 x 2.

#### 3. Find factors of 64 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 64 would be the two numbers which, when multiplied, give 64 as the result.

The following table represents the calculation of factors of 64 in pairs:

Factor Pair Pair Factorization
1 and 64 1 x 64 = 64
2 and 32 2 x 32 = 64
4 and 16 4 x 16 = 64
8 and 8 8 x 8 = 64

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 64. They are called negative pair factors.

Hence, the negative pairs of 64 would be ( -1 , -64 ) , ( -2 , -32 ) , ( -4 , -16 ) and ( -8 , -8 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 64 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 64.
• Every number is a factor of zero (0), since 64 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 8, 16, 32, 64 are exact divisors of 64.
• Factors of 64 are 1, 2, 4, 8, 16, 32, 64. Each factor divides 64 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64 are all less than or equal to 64.

• What are the prime factors of 64?

The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Prime factors of 64 are 2, 2, 2, 2, 2, 2.

• What is the sum of all factors of 64?

The sum of all factors of 64 is 127.

• What are the pair factors of 64?

Pair factors of 64 are (1,64), (2,32), (4,16), (8,8).

• What two numbers make 64?

Two numbers that make 64 are 2 and 32.

• What are multiples of 64?

First five multiples of 64 are 128, 192, 256, 320.

• Is 64 a perfect square?

Yes 64 is a perfect square.

• Which is greatest factor of 64?

The greatest factor of 64 is 32.

• How do you factors of 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64.

• What are five multiples of 64?

First five multiples of 64 are 128, 192, 256, 320, 384.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Even factors of 64 are 2, 4, 8, 16, 32, 64.
Hence, product of even factors of 64 is; 2 x 4 x 8 x 16 x 32 x 64 = 2097152.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 64? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 16, 32, 64.
Negative factors are -1, -2, -4, -8, -16, -32, -64.

How many factors are there for 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64.
So there are in total 7 factors.

Sammy is puzzled while calculating the prime factors of 64. Can you help him find them?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Prime factors of 64 are 2, 2, 2, 2, 2, 2

Joey wants to write all the prime factors of 64 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 64 are 2, 2, 2, 2, 2, 2.
So in exponential form it can be written as 26.

What is prime factorization of 64?

Prime factorization of 64 is 2 x 2 x 2 x 2 x 2 x 2 = 26.

Can you help Rubel to find out the product of the even factors of 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Even factors of 64 are 2, 4, 8, 16, 32, 64.
Hence, product of even factors of 64 is; 2 x 4 x 8 x 16 x 32 x 64 = 2097152.