Definition of factors of 96: If a number completely divides 96 without leaving a remainder, then that number is called a factor of 96. Thus, we can say that the factors of 96 are the divisors of 96.
In this article, we will learn about the factors of 96 and the prime factors of 96.
- 96 = 2×2×2×2×2×3 = 25×3 is the prime factorization of 96
- The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96
- The prime factors of 96 are 2 and 3
- Negative factors of 96 are –1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48 and -96
Table of Contents
What are the Factors of 96?
Let us write the number 96 multiplicatively in all possible ways. We definitely have:
96 = 1×96
96 = 2×48
96 = 3×32
96 = 4×24
96 = 6×16
96 = 8×12
As there are no other ways we can write 96 multiplicatively, so we will stop right now. So the factors of 96 in pairs are given as follows:
| 96 = a×b | Factors in Pairs (a,b) |
| 96 = 1×96 | (1, 96) |
| 96 = 2×48 | (2, 48) |
| 96 = 3×32 | (3, 32) |
| 96 = 4×24 | (4, 24) |
| 96 = 6×16 | (6, 16) |
| 96 = 8×12 | (8, 12) |
Thus the pair factors of 96 are (1, 96), (2, 48), (3, 32), (4, 24), (6, 16), and (8, 12). As all the numbers appearing in pair factors are the factors of 96, we conclude that
|
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. |
Number of Factors of 96
From above we have calculated the factors of 96 which are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Thus the total number of factors of 96 is twelve.
Prime Factors of 96
Note that the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 96 are 2 and 3.
Question: What are the factors of 96?
Video Solution:
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How to Find Factors of 96?
Now we will determine the factors of 96 by division method. In this method, we will try to find the numbers that can divide 96 with no remainder. See that
96/1=96 and the remainder is 0.
∴ 1 and 96 are factors of 96.
96/2=48 and the remainder is 0.
∴ 2 and 48 are factors of 96.
96/3=32 and the remainder is 0.
∴ 3 and 32 are factors of 96.
96/4=24 and the remainder is 0.
∴ 4 and 24 are factors of 96.
96/6=16 and the remainder is 0.
∴ 6 and 16 are factors of 96.
96/8=12 and the remainder is 0.
∴ 8 and 12 are factors of 96.
Note that no numbers other than the numbers in violet color can divide 96. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. are the complete list of factors of 96.
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