Factor of 40 Using Prime Factorization
Factors of 40
What are the Factors of 40?
Integers that divide 40 without leaving any remainders are known as factors of 40.
For Example: 4 is a factor of 40 because when we divide 40 by 4 it leaves the quotient as 10 and remainder as 0. Here quotient is also a factor of 40.
So to check if the number is a factor of 40 or not, divide 40 by that number and verify that the remainder is zero or not.
Factor List of 40
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.
Prime Factors of 40
The number 40 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 40 by its smallest prime factor, that is, 2.
40 ÷ 2 = 20
Again divide it by 2;
20 ÷ 2 = 10
10 ÷ 2 = 5
Now, divide by it the next prime numbers, that is, 3, 5, 7 and so on.
5 ÷ 3 = 1.67, not a factor
So, divide by the next prime number; that is, 5.
5 ÷ 5 = 1
So, the prime factorization of 40 = 2 × 2 × 2 × 5
\(=2^3~\times~5\)
This means 2 and 5 are the only prime factors of 40.
Pair Factors of 40
The pair factors are two factors that when multiplied together give a result as the original number.
Example: (2, 20) is the factor pair of 40.
The pair factors can be a positive pair or a negative pair.
Positive Factor Pairs of 40
When two positive numbers are multiplied the product is positive.
Hence, the positive pair factors of 40 are (1, 40), (2, 20), (4, 10) and (5, 8).
Read More:
Rapid Recall
Factors of 40 are;
Solved Examples
Example 1: Find the common factor of 40 and 18.
Solution:
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 18 = 1, 2, 3, 6, 9 and 18
Therefore, the common factors of 40 and 18 are 1 and 2.
Example 2: Find the common factors of 40 and 70.
Solution:
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, and 70
Therefore, the common factors of 40 and 70 are 1, 2, 5, and 10.
Example 3: Find the common factors of 40 and 80.
Solution:
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
Therefore, the common factors of 40 and 80 are 1, 2, 4, 5, 8, 10, 20 and 40.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.
So, the least factor of 40 is 1 and the greatest factor is 40 itself.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.
Sum of factors = 1 + 2 + 4 + 5 + 8 + 10 + 20 + 40 = 90
So, the sum of factors of 40 is 90.
No, 15 is not a factor of 40. Because when the number 15 divides 40, it leaves the quotient as 2 and the remainder as 10. As the remainder is not zero therefore it is not a factor.
The prime factorization of 40 = 2 × 2 × 2 × 5 or \(2^3~\times~5\).
The positive pair factors of 40 are
(1, 40), (2, 20), (4, 10) and (5, 8).