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 factorized.

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

How to find Prime Factors of 64 by Division Method?

As we know the number 64 is a composite number and it must have 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 equal 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 are:

(-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.

2. 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.

3. 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

Solution:

1. 74 cannot be completely divided by 9.

Hence, 9 is not a factor of 74.

2. 84 cannot be completely divided by 7

Hence, 7 is not a factor of 84.

3. Find all the factors of 42.

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

Hence, the 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

The Features of a Factor

• Every number has a factor and they have properties, a few of which are discussed below.

• There are an infinite number of factors for any given number.

• Any given factor of a number should always be equal to or less than the number itself.

• Every number has at least two factors, except 0 and 1. Those are usually the number itself and 1. Though these are very much the small factors.

• To find any factor, multiplication and division are used.

Fun Factor Facts

• Factors for any given number are always whole numbers and seldom fractions or decimals.

• 2 is the factor for all the given even numbers.

• 5 will always be one of the factors for all the numbers ending with 5.

• The numbers that are greater than 0 and end with 0 will always have 2,5,10 as factors.

• Through factoring, algebraic expressions are simplified and solved.

Difference between Factors and Multiples

• The terms multiples and factors are usually confused with each other. But both denote different meanings in the field of mathematics. To understand better let us take an example: The multiples of 15 are 30, 45 and 60 and many more, whereas the factors of 15 are 3 and 5.

• An exact division of a given number is called a factor. Whereas multiple is the result we achieve when we multiply the number with any given number.

• The number of factors any number can have is finite. Whereas the number of multiples any number can have are infinite.

• The factor obtained is always less than or equal to the given number. Whereas the multiples are always greater than or equal to the given number.

• A factor can also be defined as the number that can be used to multiply to get another number. Multiples can also be defined as the resulting product one gets by multiplying the number by any other integer.

• The operation used to receive the factors of a number is division. Whereas the operation used to receive the multiples is multiplication.