Factors of 96

Factors are those, which on multiplication gives the number which we require. There are different methods to find the factors of the given number. We can find factors by factorization method, by division method, by divisibility method, and by the prime factorization method. The factors of a number 96 are those numbers which on multiplication with each other gives us the number 96. The factors of 96 can be positive numbers or negative numbers. Fractions and decimal numbers are not considered as factors. However,  negative numbers are considered as factors because on multiplying two negative numbers we get a positive number.


Factors of 96 By Division

96 ÷ 1 = 96

96 ÷ 2 = 48

96 ÷ 3 = 32

96 ÷ 4 = 24

96÷ 5 = not divisible

96 ÷ 6 = 16

96÷ 7 = not divisible

96 ÷ 8 = 12

96 ÷ 9 = not divisible

96 ÷ 10 = not divisible

96÷ 11 = not divisible

96 ÷ 12 = 8

96÷ 13 = not divisible

96 ÷ 14 = not divisible

96 ÷ 15 = not divisible

96 ÷ 16 = 6

96 ÷ 17 = not divisible

96 ÷ 18 = not divisible

96 ÷ 19 = not divisible

96÷ 20 = not divisible


Divisibility Method

In this method, we will find the factors by checking its divisibility. 

Step 1: The first step is to write the number for which we need to find the factors.

Step 2: For finding the factors of 96 we will check if 96 is divisible by 2 or not. 

Step 3: If it is divisible by 2 then we have to divide it. Here 96 is divisible by 2 because it divides 96 completely.

Step 4: Now we will check whether it is divisible by 3 here 96 is also divisible by 3 by the divisibility rule.

Step  5: Since 96 is divisible by 2 it is also divisible by 4.

Step 6: 96 has 6 in its units place so by the divisibility rule it is not divisible by 5 because the number is divisible by 5 only if it has 5 or 0 in the units place.

Step 7: 96 is also divisible by 6 by checking the divisibility.

Step 8: Now by the divisibility test, 96 is not divisible by 7 as we divisible a decimal number on dividing.

Step 9: The number 96 is also divisible by 8 because it divides it completely.

Step 10: 96 is not divisible by 9 because by dividing 96 by 9 we are getting a remainder.

Step 11: It is also not divisible by 10 as it does not contains 0 in the units place.


Example:


Positive Factors of 96 can be Given as

96 = 1 × 96

96 = 2 × 48

96 = 3 × 32

96 = 4 × 24

96 = 6 × 16

96 = 8 × 12


The positive Factors of 96 

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96


Similarly, we will have negative factors of 96. 


The Negative Factors of 96

-1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -96


Prime Factorization

The prime factors of a number are the prime numbers which on multiplication gives us the original number. This is the simplest way to find the factors.

FAQ (Frequently Asked Questions)

1. How to Find Factors of 96 Using the Factorization Method?

Answer: In this method, we first find one set of factors then we find more multiplies of that number to get more factors if possible.


So in this method, we will get positive pairs and negative pairs of factors.


Steps to find the factors of 96

  1. First, we will write the number for which, we have to find the factors.

  2. Then we will find the two numbers which on multiplication give us 96.

  3. Suppose the first two factors of 96 are 2,48  because on multiplication of 2 and 48 it gives 96.

  4. Now we will find the factors of 2 since 2 has only two factors 1 and 2 itself so it cannot be further factories.

  5. Further, we will find the factors of 48 we will get

            48 = 2×2×2×2×3×1

  1. So the factors of 96 can be written as

             96 = 2×2×2×2×2×3×1

2. How to Find Factors of 96 Using the Prime Factorization Method?

Answer: The prime factors of a number are the prime numbers which on multiplication gives us the original number.


Steps to find factors of 96 using prime factorization method

  1. Consider the number for which we have to find factors here we will consider 96.

  2. Next, we will divide 96 by the smallest prime number that is 2.

            96÷2 = 48

  1. Now again we will divide 48 by 2 

            48÷2= 12

  1. We will continue this procedure until it is dividing by 2.

            12÷2 =6

              6÷2 = 3

  1. Now factor 3 on dividing with 2 will give us a decimal number which is not allowed in factors. So we will consider the next prime number that is 3.

             3÷3 =1

  1. So now finally we get the number 1 which cannot be further divided by any number. So, we will stop the procedure here. 

  2. So, the factors of 96 by prime factorization can be written as 2 × 2 × 2 × 2 × 2 × 3. This can also be written as 2⁵ and 3¹ where 2 and 3 are prime numbers.