Factor of 90 Using Prime Factorization
Factors of 90
What are the Factors of 90?
Integers that divide 90 without leaving any remainder are known as the factors of 90.
Example: 5 is a factor of 90 because when we divide 90 by 5, it gives us the quotient as 18 and the remainder as 0. Here the quotient, 18, is also a factor of 90.
So, to check if any number is a factor of 90 or not, divide 90 by that number and verify that the remainder is zero or not.
Factor List of 90
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Prime Factors of 90
The number 90 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 90 by its smallest prime factor, that is, 2.
90 ÷ 2 = 45
Again, divide it by 2;
45 ÷ 2 = 22.5, not a factor.
Now, divide it by the next prime numbers, that is, 3, 5, 7, and so on.
45 ÷ 3 = 15
15 ÷ 3 = 5
Again, divide by the next prime number, that is, 5.
5 ÷ 5 = 1
So, the prime factorization of 90 = 2 × 3 × 3 × 5
= 2 × \(3^2\) × 5
Therefore, 2, 3, and 5 are the prime factors of the number 90.
Factor Pairs of 90
The factor pairs of a number are two factors whose product is the number itself.
Example: (2, 45) is the factor pair of 90.
The factor pair can be a positive pair or a negative pair.
Positive Pair Factors of 90
[Note: When two positive numbers are multiplied, the product is positive.]
Hence, the positive pair factors of 90 are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), and (9, 10).
Read More:
Rapid Recall
Factors of 90 are;
Solved Examples
Example 1: Find the common factors of 18 and 90.
Solution:
Factors of 18 = 1, 2, 3, 6, 9, and 18.
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Therefore, the common factors of 18 and 90 are 1, 2, 3, 6, 9, and 18.
Example 2: Find the common factors of 90 and 10.
Solution:
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Factors of 10 = 1, 2, 5, and 10
Therefore, the common factors of 90 and 10 are 1, 2, 5, and 10
Example 3: Find the common factors of 97 and 90.
Solution:
Factors of 97 = 1 and 97.
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Therefore, the common factor of 97 and 90 is 1.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
So, the least factor of 90 is 1, and the greatest factor is 90 itself.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Sum of the factors = 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234
So, the sum of factors of 90 is 234.
Yes, 15 is a factor of 90. This is because when the number 15 divides 90, it leaves the quotient as 6 and the remainder as 0.
The prime factorization of 90 is 2 × 3 × 3 × 5 or 2 × \(3^2\) × 5.
The positive pair factors of 90 are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), and (9, 10).