Definition of factors of 108: If a number completely divides 108 without leaving a remainder, then that number is called a factor of 108. Thus, we can say that the factors of 108 are the divisors of 108.
Here, we will learn about the factors of 108 and the prime factors of 108.
- 108 = 2×2×3×3×3 = 22×33 is the prime factorization of 108
- The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108
- The prime factors of 108 are 2 and 3
- Negative factors of 108 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54 and -108
Table of Contents
What are the Factors of 108?
Let us write the number 108 multiplicatively in all possible ways. We definitely have:
108 = 1×108
108 = 2×54
108 = 3×36
108 = 4×27
108 = 6×18
108 = 9×12
As there are no other ways we can write 108 multiplicatively, so we will stop right now. So the factors of 108 in pairs are given as follows:
| 108 = a×b | Factors in Pairs (a,b) |
| 108 = 1×108 | (1, 108) |
| 108 = 2×54 | (2, 54) |
| 108 = 3×36 | (3, 36) |
| 108 = 4×27 | (4, 27) |
| 108 = 6×18 | (6, 18) |
| 108 = 9×12 | (9, 12) |
Thus the pair factors of 108 are (1, 108), (2, 54), (3, 36), (4, 27), (6, 18), and (9, 12). As all the numbers appearing in pair factors are the factors of 108, we conclude that
|
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. |
Number of Factors of 108
From above we have calculated the factors of 108 which are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Thus the total number of factors of 108 is twelve.
Prime Factors of 108
Note that the factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. Among these factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 108 are 2 and 3.
Question: What are the factors of 108?
Video Solution:
How to Find Factors of 108?
Now we will determine the factors of 108 by division method. In this method, we will try to find the numbers that can divide 108 with no remainder. See that
108/1=108 and the remainder is 0.
∴ 1 and 108 are factors of 108.
108/2=54 and the remainder is 0.
∴ 2 and 54 are factors of 108.
108/3=36 and the remainder is 0.
∴ 3 and 36 are factors of 108.
108/4=27 and the remainder is 0.
∴ 4 and 27 are factors of 108.
108/6=18 and the remainder is 0.
∴ 6 and 18 are factors of 108.
108/9=12 and the remainder is 0.
∴ 9 and 12 are factors of 108.
Note that no numbers other than the numbers in violet color can divide 108. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. are the complete list of factors of 108.
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