Factors of 64

Pair Factors of 64

The pair factor of 64 is defined as the number that obtains the original number 64 when two numbers are multiplied together. For example, the factor pairs of 64 are written as (1,64) and (-1,-64). When we multiply the pair of two negative numbers, the result obtained is the original number such as multiplying -1 × -64 = 64. Hence, we can consider both negative and positive factors of 64. Factor pairs of number 64 can be either positive or negative numbers but not a fraction or division. In this article. We will study factors of 64, pair factors of 64, how to find factors of 64, prime factorization of 64, all factor pairs of 64 etc.


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How to Find the Factors of 64?

Here are the steps to find the factors of 64.

  1. The first step is to write the number 64.

  2. Find any two numbers which when multiplied give the original number 64. For example, 2 ×32= 64.

  3. As, we know 2 = 2 × 1 is a prime number as it has only two factors 1 and 2 which cannot be further factorised.

  4. But you can see 32 is a composite number as it has more than 2 factors and it can be further factorized.

  5. Factors of 32 are 2 ×2 × 2 ×2 × 2 × 1 

  6. Hence, the factors of 64 are 2 × 2 × 2 × 2 × 2 × 2 × 1 .

  7. Finally at the last, we will write all the possible numbers that can be obtained from 2 ×2 × 2 × 2 ×2 × 2 × 1.


Factors of 64 are


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


How to Find Prime Factors of 64 by Division Method?

As we know the number 64 is a composite number and it must be having prime factors. Now, let us learn how to calculate the prime factors of 64.


1. The first step is to divide the number 64 with the smallest prime factor such as 2


64 ÷ 2 = 32.


2. Now divide 32 by 3 and repeat the same process till you get the quotient equals to 1.

  •   32 ÷ 2 = 16

  •    16 ÷ 2= 8

  •    8 ÷ 2=4

  •    4 ÷ 2 = 2

  •    2 ÷2 =1

Finally, we got the number 1 at the last step of the division process. Now, we cannot proceed further. So the prime factors of 64 are 2 × 2 × 2 × 2 × 2 or 26, where 2 is the smallest prime number.


We can also find the exact factors of a number 64 through the prime factorization method. The prime factor of 64 is 26 .  The exponent in prime factorization is 6. Now, when we add the number 1 with the exponent 6 , we get 7 i.e  6 + 1 - = 7.


Hence the number 64 has 7 factors.


Pair factors of 64

We will find the pair factors of 64 by multiplying the two numbers in a pair that will ultimately obtain the original number 64.


Positive pair factors of 64 are

(1,64)

(2, 32)

(4, 16)

(8, 8)


Negative pair factors of 64

(-1,-64)

(-2, -32)

(-4, -16)

(-8, -8)


All Factors Pair of 64

Here, you can see  all factors pair of 64 


(1,64) are factors of 64 as 1 ×64 is 64

(2, 32) are factors of 105 as 2 × 32 is 64

(4, 16) are factors of 105 as 4 ×16 is 64

(8, 8) are factors of 105 as 8 × 8 is 64


Factor Tree of 64

One procedure to calculate the prime factorization of a number is to make a factor tree. In factor trees, the factors of numbers are first identified and then those numbers are further factored until we reach closure. 


The first step of drawing a factor tree is to find the pairs of a factor whose product of the numbers we are factoring. These two factors are placed at the first branch of the factor tree. There are primarily multiple pairs of factors that we chose to start the process. We repeat the process with each factor until every branch of the tree ends in a prime number.


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Solved Examples

1. Mention all the factors of 20, 36, and  60, 


Solution:

  1. Factors of 20 are 1 × 20 =20,  10 ×2= 20 and 4 × 5= 20

Hence, the factors of 20 are 1,2,4,5 and 20.


  1. Factors of 36 are 1×36 = 36, 18 × 2 =36 , 4 × 9 = 36

Hence, the factors of 36 are 1, 2, 3, 4, 6, 9 and 36.


  1. 60

Factors of 60 are 1×60=60 , 2×30 =60, 20× 3= 60, 4 × 15=60


Hence, the factors of 60 are 1,2,3,4,5,6,10,12,15 and 60.


2. Verify if,

  1. 9 is a factor of 74

  2. 7 is a factor of 84


  1. 74 cannot be completely divided by 9.

Hence, 9 is not a factor of 74.


  1. 84 cannot be completely divided by 7

Hence, 7 is not a factor of 84.


3. Find all the factors of 42.


Factors of 42 are - 21 ×2 = 42 , 14 × 3 = 42, 7 × 6 = 42


Hence factors of 42 are 2,3,6,7,21,and 42

 

Quiz Time

1. The largest factor of a number is

  1. 1

  2. 2

  3. Number itself


2.  The highest common factors of a number 72 and 56 are

  1. 7

  2. 3

  3. 2

  4. 8


3.   What are the first four factors of 80 in a proper sequence? 

  1. 1,2,3,4,5

  2. 1,2,4,5,8

  3. 1,3,5,10,20

  4. 1,2,3,5,10


4. What are the factors of 50?

  1. 1, 2, 5,10,25,50

  2. 1, 2, 4, 10, 25, 50

  3. 1,2,5,10,24

  4. 1, 2,3,4,510,25,50

FAQ (Frequently Asked Questions)

1. Explain the Meaning of Prime Factorization and Prime Factors?

Prime Factorization - It is a method of finding prime factors of a given number, say a composite number. The factors are nothing but are known as prime numbers. The  prime numbers are those numbers that  include only two factors i.e. one and number itself. For example prime factors of 64 are 2 × 2 × 2 ×2 × 2 ×2 × 1 .= 64 and 2 is a prime number..


Prime factorization of 64 = 2⁶ 


Whereas the composite numbers are the numbers that include more than 2 factors. For example, 6 =1 × 2 × 3 is a  composite number as it has more than two factors.

2. What is Known as the Highest Common Factor?

The highest number which is the factor of two or more than two numbers is known as the highest common factor or greatest common factor.


When we find all the factors of two or more than two numbers, there are few factors which are common in both, the largest common factor that is found in the common factors is known as the highest common factor or greatest common factor.

 

For example, the highest common factor of 18 and 21 is 3


Factors of 18  are  = 2 ×3 ×3

Factors of 21 are = 3 ×7


Here, we can see 3 is a  common factor in 18 and 21.