Factors of 64 | With Easy Division and Prime Factorization

Factors of 64

In mathematics, factors of 64 are the natural numbers that divide a number evenly.

For example:

64 divided by 2 equals 32, so 2 is a factor of 64. Two factors are called pair factors if they can result in the original number when multiplied together.

 We can determine the factors of 64 using the factorization method.

What are the Factors of -64?

When we multiply two numbers, and we get -64 as a product, those numbers are the factors of -64. 

Here is the explanation:

-1 × 64 = -64

 1  × -64 = -64

-2 × 32 = -64

 2 × -32 = -64

-4 × 16 = -64

 4 × -16 = -64

-8 × 8 = -64

 8  ×  -8 = -64

We can get -64 by having (-1, 64), (-2, 32), (-4, 16), and (-8, 8) as a pair of factors. Similarly, we can also get -64 by having (1, -64), (2, -32), (4, -16), and (8, -8) as a pair of factors.

Pair Factors of 64

In order to find the pair factors of 64, multiply the two numbers in the pair to get 64, as follows:

Positive pair factors

If,

1 × 64 = 64, (1, 64) 

2 × 32 = 64, (2, 32) 

4 × 16 = 64, (4, 16) 

8 × 8 = 64, (8, 8) 

Hence, the positive pairs are (1, 64), (2, 32), (4, 16), and (8, 8).

Negative pair factors

Similarly, to determine the negative pair factors for 64, follow the steps below:

-1 × -64 = 64, (-1, -64) 

-2 × -32 = 64, (-2, -32) 

-4 × -16 = 64, (-4, -16) 

-8 × -8 = 64, (-8, -8) 

As a result, the negative pair factors are (-1, -64), (-2, 32), (-4, 16) and (-8, 8).

How to calculate the Factors of 64?

To determine the factors of 64, we must divide the original number by all the natural numbers from 1 to 64. A number that completely divides 64 without leaving any remainder is a required factor. 

64 ÷ 1 = 64

64 ÷ 2 = 32

64 ÷ 4 = 16

64 ÷ 8 = 8

64 ÷ 16 = 4

64 ÷ 32 = 2

64 ÷ 64 = 1

Factors of 64 are1, 2, 4, 8, 16, 32, and 64.

Prime Factors of 64 By Division Method

There should be prime factors in the number 64, as it is a composite number.

 How do we calculate the prime factors of a number 64?

Step 1: The first step is to divide 64 by the smallest prime factor, say 2.

64 ÷ 2 = 32

Step 2: Repeat Step 1 by dividing 32 by 2.

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

As a result of the division process, we received the number 1. Therefore, we cannot proceed. Thus, the prime factors of 64 are equivalent to 2 x 2 × 2 x 2 x 2 x 2 or 26, where 2 is a prime number.

It is possible to determine how many factors there are in a number 64 by using prime factorization. 26 is the prime factor of 64. 6 is its exponent in prime factorization. By adding 1 to the exponent 6, 

we get 7, i.e.,  

6 +1 = 7. 

Therefore, there are 7 factors in the number 64.

Solved Examples

Q.1: What is the sum of all the factors of 64 and 24? Is it odd or even?

Solution: 1, 2, 4, 8, 16, 32,, and 64 are the factors. If we add these factors together, we get;

1+2+4+8+16+32+64 = 127

Therefore, 127 is an odd number.

Factors of 24
= 1, 2, 3, 4, 6, 8, 12, and 24.

if we add them

1+2+3+4+6+8+12+24=60

Q.2: A blackboard is 64 square centimeters in size. Determine its width given the board’s length of 8 cm.

Solution: 

Given,

Area of the board = 64 sq cm.

Length = 8 cm

It is possible to have a rectangular or square board.

Thus, the area will be equal to the product of length and width.

Area = length x width

Width = area ÷ length

= 64 ÷ 8

= 8

Therefore, the width is 8 cm as well. Thus, the blackboard has a square shape.

Q.3: Jack studies four hours a day. How many days will he complete 64 hours?

Solution:

 Number of hours Jack studies daily = 4 hours

Total number of hours = 64 hours

Therefore, 

Number of days to cover 64 hours = 64/4 = 16

As a result, Jack will cover 64 hours of schooling if he studies 4 hours for 16 days.

Q.4: Identify the common factors among 41, 75, and 68.

Solution: Write down the factors of each number here in order to determine the common factor.

Factors of 41 are 1 and 41.

The prime factor of 75 is 1, 3, 5, 15, 25, and 75.

Factors of 68 = 1, 2, 4, 17, 34, and 68.

Common factors = 1.

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