Factors of 90

Factors of 90 are the numbers, which gives the result as 90 when multiplied together in pair of two. Apart from this number, there are other numbers which are commonly used in mathematical calculations, such as factors of 24, 36, 100, 105, 900, etc. Prime factorisation of 90 will give us results in prime numbers. To find the factors of a number say 90, we will use the multiplication method. We will find here the factors in pair as well as prime factorisation, in this article.

Pair Factors of 90

We can find the pair factors of number 90, by multiplying two numbers in a pair to get the original number as 90, such as;

1 × 90 = 90

2 × 45 = 90

3 × 30 = 90

5 × 18 = 90

6 × 15 = 90

9 × 10 = 90

Therefore, the pair factors of 90 are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15) and (9, 10).

Prime Factors of 90

The number 90 is a composite number. Now let us find the prime factors of 90.

• The first step is to divide the number 90 with the smallest prime factor,i.e. 2 and divide the output again by 2 till you get a fraction or odd number.

90 ÷ 2 = 45;

• Divide 45 by 2.

45 ÷ 2 = 22.5; fraction cannot be a factor.

         Therefore, moving to the next prime numbers, 3, 5, 7 and so on.

• Divide 45 by 5.

45 ÷ 3 = 15

15 ÷ 3 = 5

• Now, we know 5 is a prime number and it has only two factors; 1 and 5. Therefore, we cannot continue with the division method further.
• So, the prime factors of 90 are 2 × 3 × 3 × 5 or 2 × 3² × 5, where 2, 3 and 5 are the prime numbers.

Sum of Factors of 90

We know that the sum of the factors of the number 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Now, to find the sum of the factors, add all the number, you will get a total of 234. It means that

Sum of factors of 90 = 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90

Sum of factors of 90 = 234

If you exclude the number 90, you will get 144. because, if you subtract 90 from 234, you will get 144

(i.e.,) 234 – 90 = 144

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