# Factors of 90

Definition of factors of 90: If a number completely divides 90 without leaving a remainder, then that number is called a factor of 90. Thus, we can say that the factors of 90 are the divisors of 90.

Here, we will learn about the factors of 90 and the prime factors of 90.

• 90 = 2×3×3×5 is the prime factorization of 90
• The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90
• The prime factors of 90 are 2, 3 and 5
• Negative factors of 90 are –1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45 and -90

#### What are the factors of 90?

Let us write the number 90 multiplicatively in all possible ways. We definitely have:

90 = 1×90

90 = 2×45

90 = 3×30

90 = 5×18

90 = 6×15

90 = 9×10

As there are no other ways we can write 90 multiplicatively, so we will stop right now. So the factors of 90 in pairs are given as follows:

 90 = a×b Factors in Pairs (a,b) 90 = 1×90 (1, 90) 90 = 2×45 (2, 45) 90 = 3×30 (3, 30) 90 = 5×18 (5, 18) 90 = 6×15 (6, 15) 90 = 9×10 (9, 10)

Thus the pair factors of 90 are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), and (9, 10). As all the numbers appearing in pair factors are the factors of 90, we conclude that

 The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.

#### Number of factors of 90

From above we have calculated the factors of 90 which are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Thus the total number of factors of 90 is twelve.

#### Prime Factors of 90

Note that the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90. Among those factors, we observe that only 2, 3 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 90 are 2, 3 and 5.

Question: What are the factors of 90?

Video Solution:

#### How to find factors of 90?

Now we will determine the factors of 90 by division method. In this method, we will try to find the numbers that can divide 90 with no remainder. See that

90/1=90 and the remainder is 0.

1 and 90 are factors of 90.

90/2=45 and the remainder is 0.

2 and 45 are factors of 90.

90/3=30 and the remainder is 0.

3 and 30 are factors of 90.

90/5=18 and the remainder is 0.

5 and 18 are factors of 90.

90/6=15 and the remainder is 0.

6 and 15 are factors of 90.

90/9=10 and the remainder is 0.

9 and 10 are factors of 90.

Note that no numbers other than the numbers in violet color can divide 90. So the numbers in violet color, that is, 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. are the complete list of factors of 90.