Factors of 96
Factors of 96 are those numbers that can divide the original number evenly and leaves no remainder. For example, if 2 is the factor of 96 then 96 divided by 2 is a whole number and not a fraction.
96 ÷ 2 = 48 [Remainder = 0]
Therefore, 2 is one of the factors.
Since 96 is a composite number, therefore it will have factors more than two. Let us learn in this article how to find the factors of ninety-six. Also, we will learn pair factors and prime factorisation of 96.
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Pair Factors of 96
To find the positive and negative factor pairs of 96, multiply the two numbers in a pair to get the original number as 96, such numbers are as follows:
| Positive Pair Factor | Negative Pair Factor |
| 1 × 96 = 96 ⇒ (1, 96) | -1 × -96 = 96 ⇒ (-1, -96) |
| 2 × 48 = 96 ⇒ (2, 48) | -2 × -48 = 96 ⇒ (-2, -48) |
| 3 × 32 = 96 ⇒ (3, 32) | -3 × -32 = 96 ⇒ (-3, -32) |
| 4 × 24 = 96 ⇒ (4, 24) | -4 × -24 = 96 ⇒ (-4, -24) |
| 6 × 16 = 96 ⇒ (6, 16) | -6 × -16 = 96 ⇒ (-6, -16) |
| 8 × 12 = 96 ⇒ (8, 12) | -8 × -12 = 96 ⇒ (-8, -12) |
How to calculate the Factors of 96?
To find the factors of the natural number, 96, we need to check by which number 96 is evenly divisible and leaves no remainder.
As we know, 1 and the number itself are the two common factors that all the integers will have apart from 1. Hence, 1 and 96 are the two factors of 96. By this, we can conclude that rest of the factors lies between 1 and 96.
- 96 ÷ 1 = 96 [Remainder = 0]
- 96 ÷ 2 = 48 [Remainder = 0]
- 96 ÷ 3 = 32 [Remainder = 0]
- 96 ÷ 4 = 24 [Remainder = 0]
- 96 ÷ 6 = 16 [Remainder = 0]
- 96 ÷ 8 = 12 [Remainder = 0]
- 96 ÷ 12 = 8 [Remainder = 0]
- 96 ÷ 16 = 6 [Remainder = 0]
- 96 ÷ 24 = 4 [Remainder = 0]
- 96 ÷ 32 = 3 [Remainder = 0]
- 96 ÷ 48 = 2 [Remainder = 0]
- 96 ÷ 96 = 1 [Remainder = 0]
Therefore,
| Factors of 96 |
| 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96 |
Prime Factors of 96
The number 96 is a composite and it should have prime factors. Now let us know how to calculate the the prime factors.
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- The first step is to divide the number 96 with the smallest prime factor, say 2.
96 ÷ 2 = 48
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- Again divide 48 by 2
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
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- Now if you divide 3 by 2, you will get a fractional number and it should not be a factor of a number. So proceed with the next prime factor, say 3.
3 ÷ 3 = 1
Finally, you received the number 1 at the end of the division process. Now, we cannot proceed further. Thus, the prime factors of 96 are written as :
2 x 2 x 2 x 2 x 2 x 3 or 3 x 25
where 2 and 3 are the prime numbers.
Solved Examples
Q.1: What is the sum of all the factors of number 96?
Solution: We know that, factors of 96 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
Now, sum of all the factors = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96
Sum = 252
Q.2: What is the average of all the factors of 96?
Solution: The factors for the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Average = (Sum of all factors) ÷ Total number of factors
= (1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96) ÷ 12
= 252 ÷ 12
= 21
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Frequently Asked Questions – FAQs
What are the factors of 96 in Maths?
What do you prime factorisation of 96?
96 = 2 × 2 × 2 × 2 × 2 × 3 = 25 × 31