The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. The factors of 8 can be positive or negative. For example, the factors of 8 can be (1, 8) or (-1, -8). If we multiply the pair of negative factors, such as multiplying -1 and -8, results in an original number 8. In this article, we will learn the factors of 8, pair factors and the prime factors of 8 using the division method and the prime factorization method with many solved examples.
Table of Contents:
- What are the Factors of 8?
- Pair Factors of 8
- Factors of 8 by Division Method
- Prime Factorization of 8
- Solved Examples
- FAQs
What are the Factors of 8?
In Mathematics, the factors of 8 are the numbers, which are multiplied in pairs resulting in an original number 8. In other words, a number that divides 8 exactly without leaving a remainder, then the number is a factor of 8. As the number 8 is an even composite number, it has many factors other than 1 and 8. Thus, the factors of 8 are 1, 2, 4 and 8.
Factors of 8: 1, 2, 4, and 8. Prime Factorization of 8: 2 × 2 × 2 or 2^{3}. |
Pair Factors of 8
A pair of numbers, which are multiplied together resulting in an original number 8 is called the pair factors of 8. As discussed above, the pair factors of 8 can be positive or negative. The positive and negative pair factors of 8 is given below:
Positive Pair Factors of 8:
Positive Factors of 8 |
Positive Pair Factors of 8 |
1 × 8 |
(1, 8) |
2 × 4 |
(2, 4) |
Negative Pair Factors of 8:
Negative Factors of 8 |
Negative Pair Factors of 8 |
-1 × -8 |
(-1, -8) |
-2 × -4 |
(-2, -4) |
Factors of 8 by Division Method
The factors of 8 can be found using the division method. In the division method, we need to find the integers which divide 8 exactly without leaving a remainder, and those integers are considered as the factors of 8. Now, let us find the factors of 8 using the division method.
- 8/1 = 8 (Factor is 1 and Remainder is 0)
- 8/2 = 4 (Factor is 2 and Remainder is 0)
- 8/4 = 2 (Factor is 4 and Remainder is 0)
- 8/8 = 1 (Factor is 8 and Remainder is 0)
If we divide 8 by any numbers other than 1, 2, 8 and 8, it leaves a remainder. Hence, the factors of 8 are 1, 2, 4 and 8.
Prime Factorization of 8
The prime factorization of 8 is the process of writing the number as the product of its prime factors. Now, let us discuss the process of finding the prime factors of 8.
We know that the pair factor of 8 is (1, 8), and keep the number 1 as it is, as the number 1 is neither prime nor composite.
Now, take the number 8, and it is a composite number, it can be further divided into its prime factors. Thus, the number 8 is written as the product of its prime factors.
(i.e) 8 = 2 × 2 × 2
Therefore, the prime factorization of 8 is 2 × 2 × 2 or 2^{3}.
The number 8 is considered as a perfect cube. We will find the exact number of factors with the help of prime factorisation. The prime factor of the 8 is 2^{3}. The exponent in the prime factorisation is 3. When you add the number 1 with the exponent, i.e.,3 +1 = 4. Therefore, the number 8 has 4 factors.
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Examples
Example 1:
Find the common factors of 8 and 7.
Solution:
The factors of 8 are 1, 2, 4 and 8.
The factors of 7 are 1 and 7.
As 7 is a prime number, the common factor of 8 and 7 is 1.
Example 2:
Find the common factors of 8 and 9.
Solution:
Factors of 8 = 1, 2, 4 and 8.
Factors of 9 = 1, 3, and 9.
Hence, the common factor of 8 and 9 is 1.
Example 3:
Find the common factors of 8 and 4.
Solution:
The factors of 8 are 1, 2, 4 and 8.
The factors of 4 are 1, 2 and 4.
Hence, the common factors of 8 and 4 are 1, 2, and 4.
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Frequently Asked Questions on Factors of 8
What are the factors of 8?
The factors of 8 are 1, 2, 4 and 8.
What is the prime factorization of 8?
The prime factorization of 8 is 2 × 2 × 2 or 2^{3}.
What are the positive pair factors of 8?
The positive pair factors of 8 are (1, 8) and (2, 4).
Write down the negative pair factors of 8.
The negative pair factors of 8 are (-1, -8) and (-2, -4).
Is 2 a factor of 8?
Yes, 2 is a factor of 8. If 8 is divisible by 2, it leaves a quotient of 4 and remainder 0, and hence 2 is a factor of 8.