Factors of 8 Using Prime Factorization
Factors of 8
What are the Factors of 8?
Integers that divide 8 without leaving any remainders are known as factors of 8.
For Example: 2 is a factor of 8 because when we divide 8 by 2, the quotient is 4 and the remainder is 0. Here the quotient is also a factor of 8.
To check if the number is a factor of 8 or not, divide 8 by that number and verify that the remainder is zero or not.
Also, we know the ‘Divisibility Rule of 8’ that is if the ‘ones’, ‘tens’ and ‘hundreds’ place is divisible by 8, then that number is divisible by 8.
Example: Let the given number be 58640.
The last three digits should be divisible by 8.
58640
The last three digits = 640
640 ÷ 8 = 80
Therefore, 58640 is divisible by 8.
Factor list of 8
The factors of 8 are 1, 2, 4, and 8.
Prime Factors of 8
The number 8 is a composite number, that is, it has more than two numbers as factors. To find the prime factors, first we will divide the number 8 by its smallest prime factor, that is, 2.
8 ÷ 2 = 4
Again divide it by 2;
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 8 = 2 × 2 × 2 or 2\( ^3 \).
This means that 2 is the prime number of the 8.
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Factor Pairs of 8
The factor pairs are two factors that when multiplied together results in the original number.
Example: (2, 4) is the factor pair of 8.
The factor pairs can be positive or negative .
Positive Factor Pairs of 8 : When two positive numbers are multiplied the product is positive.
Hence, the positive Factor pairs of 8 are (1, 8) and (2, 4).
Rapid Recall
Factors of 8 are ;
Solved Examples
Example 1: Find the common factor of 8 and 10.
Solution:
Factors of 8 = 1, 2, 4, and 8
Factors of 10 = 1, 2, 5, and 10
Therefore, the common factors of 8 and 10 are 1 and 2.
Example 2: Find the common factors of 8 and 12.
Solution:
Factors of 8 = 1, 2, 4, and 8
Factors of 12 = 1, 2, 3, 4, 6, and 12
Therefore, the common factors of 8 and 12 are 1, 2, and 4.
Example 3: The teacher brought a cake to the classroom and cut it into 8 pieces. How will she divide the cake equally among 4 children?
Solution:
Number of pieces = 8
Number of children = 4
Each child will get = number of pieces number of children
= 8 \( \div \) 4
= 2
Therefore, the teacher will give each child 2 pieces of the cake.
The factors of 8 are 1, 2, 4, and 8
So, the least factor of 8 is 1 and the greatest factor is 8 itself.
The factors of 8 are 1, 2, 4, and 8.
Sum of factors = 1 + 2 + 4 + 8 = 15
So, the sum of factors of 8 is 15.
No, 6 is not a factor of 8. Because when the number 6 divides 8, the quotient is 1 and the remainder is 2. As the remainder is not zero, 6 is not a factor of 8.
The prime factorization of 8 is 2 × 2 × 2 or 2\( ^3 \).
The negative factor pairs of 8 are (–1,-8) and (-2, -4).