If a number completely divides 8 with the remainder zero, then that number is called a factor of 8. Note that the factors of 8 are 1, 2, 4, and 8. We will learn about the factors of 8 and the prime factors of 8 here.
Table of Contents
Highlights of Factors of 8
- 8=2×2×2 is the prime factorization of 8.
- The factors of 8 are 1, 2, 4, and 8.
- The only prime factor of 8 is 2.
- Negative factors of 8 are –1, -2, -4, and –8.
What are the Factors of 8?
At first, we will find all the factors of 8 by the multiplication method. To do that, we need to write the number 8 multiplicatively in all possible ways. We have:
| 8 = 1×8 | ∴ 1, 8 are factors of 8 |
| 8 = 2×4 | ∴ 2, 4 are factors of 8 |
We can see that it is not possible to express 8 multiplicatively in any other way. So we will stop right now. We have obtained all the factors of 8 which are in brown color.
∴ the factors of 8 are 1, 2, 4, and 8.
As d is a factor of 8 if and only if -d is a factor of 8, we get all the negative factors of 8. They are -1, -2, -4, and -8.
Pair Factors of 8
| 8 = a×b | Factors in Pairs (a,b) |
| 8 = 1×8 | (1, 8) |
| 8 = 2×4 | (2, 4) |
Thus the positive pair factors of 8 are (1, 8) and (2, 4).
To find the negative factors of 8, we will use the following fact: (a, b) is a positive factor of 8 if and only if (-a, -b) is a negative factor of 8. Thus all the negative pair factors of 8 are (-1, -8) and (-2, -4).
Number of Factors of 8
From above we have calculated the factors of 8 which are 1, 2, 4, and 8. Thus the total number of factors of 8 is four.
Prime Factors of 8
Note that the factors of 8 are 1, 2, 4, and 8. Among those factors, we observe that only 2 is a prime number as 2 does not have any proper divisors.
∴ the only prime factor of 8 is 2.
Also Read:
| Factors of 12: | 1, 2, 3, 4, 6, 12 |
| Factors of 16: | 1, 2, 4, 8, 16 |
| Factors of 20: | 1, 2, 4, 5, 10, 20 |
| Factors of 24: | 1, 2, 3, 4, 6, 8, 12, 24 |
Question: What are the factors of 8?
Video Solution:
How to find factors of 8?
Now we will determine the factors of 8 by division method. In this method, we will find the numbers that can divide 8 with no remainder. We have:
| 8/1=8 and the remainder is 0 | ∴ 1 and 8 are factors of 8 |
| 8/2=4 and the remainder is 0 | ∴ 2 and 4 are factors of 8 |
Note that no numbers other than the numbers 1, 2, 4, and 8 can divide 8. Thus 1, 2, 4, and 8 are the complete list of factors of 8.
Related Topics:
FAQs on Factors of 8
Ans: The factors of 8 are 1, 2, 4, and 8. These are the positive factors of 8. The negative factors of 8 are -1, -2, -4, and -8.
Ans: The sum of the factors of 8 is 1+2+4+8=15.
Ans: No, 3 is not a factor of 8.
Ans: The product of factors of 8 is 1×2×4×8 = 64.
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.