The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. If a number completely divides 100 without leaving a remainder, then that number is called a factor of 100. Here, we will discuss the factors of 100 and the prime factors of 100. We have:
- 100 = 2×2×5×5 = 22×52 is the prime factorization of 100.
- The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- The prime factors of 100 are 2 and 5.
- Negative factors of 100 are -1, -2, -4, -5, -10, -20, -25, -50, and -100.
Table of Contents
What are the factors of 100?
Let us write the number 100 multiplicatively in all possible ways. We definitely have:
100 = 1×100
100 = 2×50
100 = 4×25
100 = 5×20
100 = 10×10
As there are no other ways we can write 100 multiplicatively, so we will stop right now. So the factors of 100 in pairs are given as follows:
| 100 = a×b | Factors in Pairs (a,b) |
| 100 = 1×100 | (1, 100) |
| 100 = 2×50 | (2, 50) |
| 100 = 4×25 | (4, 25) |
| 100 = 5×20 | (5, 20) |
| 100 = 10×10 | (10, 10) |
Thus the pair factors of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10). As all the numbers appearing in pair factors are the factors of 100, we conclude that
| The factors of 100 are: 1, 2, 5, 10, 20, 50, and 100. |
Number of factors of 100
From above we have calculated the factors of 100 which are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Thus the total number of factors of 100 is nine.
Prime Factors of 100
We know that the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among those factors, we observe that only 2 and 5 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 100 are 2 and 5.
Question: What are the factors of 100?
Video Solution of factors of 100:
How to find factors of 100?
Now we will determine the factors of 100 by division method. In this method, we will try to find the numbers that can divide 100 with no remainder. See that
100/1=100 and the remainder is 0.
∴ 1 and 100 are factors of 100.
100/2=50 and the remainder is 0.
∴ 2 and 50 are factors of 100.
100/4=25 and the remainder is 0.
∴ 4 and 25 are factors of 100.
100/5=20 and the remainder is 0.
∴ 5 and 20 are factors of 100.
100/10=10 and the remainder is 0.
∴ 10 and 10 are factors of 100. ⇒ 10 is a factor of 100.
Note that no numbers other than the numbers in violet color can divide 100. So the numbers in violet color, that is, 1, 2, 4, 5, 10, 20, 25, 50, and 100 are the complete list of factors of 100.
Also Read:
FAQs on Factors of 100
Ans: The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Ans: The pair factors of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).
Ans: The prime factorization of 100 is 100 = 2×2×5×5 = 22×52.
This article is written by Dr. T, an expert in Mathematics (PhD). On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.