Factors of 45 | Find Factors With Easy Division & Prime Factorization

Factors Of 45

In mathematics, the factors of 45 are the pairs of numbers that, when multiplied together, give 45. 

For example,

By multiplying 2 and 3, we get 6, which means 2 and 3 are factors of 6. Similarly, you can find all the factors in 45. 

What are the Factors of 45?

The factors of 45 are numbers that divide the original number completely or uniformly. When multiplied in pairs, the numbers that give the result of 45 are called pair factors.

When we divide 84 by any of its factors, the result will be a whole number. The composite numbers 45, 36, 18, 60, 42, 30, 90, etc. have more than two factors.

I can use the simple multiplication method and the division method to find the factors of a number and the prime factors.

What are the Factors of -45?

When we multiply two numbers and get -45 as a product, those numbers are the factors of -45. 

Here is the explanation:

-1 × 45 = -45

 1 × -45 = -45

 -3 × 15 = -45

 3 × -15 = -45

 -5 × 9 = -45

 5 × -9 = -45

We can get -45 by having (-1, 45), (-3, 15), and(-5, 9) as a pair of factors. Similarly, we can also get -45 by having (1, -45), (3, -15), and(5, -9)as a pair of factors.

How to Find the Factors of 45?

You will learn how to find the factors of 45 by using the division method in this section. 

In this method, the divisor and quotient of 45 are treated as factors of 45 when we divide it by natural numbers 1, 2, 3, etc.

Here is the result of dividing 45.

45/1 = 45 × 1 + 0 {remainder = 0, so 1 and 45 are factors}

45/2 = 22 × 2 + 1 {remainder ≠ 0, so 2 and 22 are not factors}

45/3 = 15 × 3 + 0 {remainder = 0,so 3 and 15 are factors}

45/4 = 11 × 4 + 1 {remainder ≠ 0, so 2 and 22 are not factors}

45/5 = 9 × 5 + 0 {remainder = 0, so 5 and 9 are factors}

45/6 = 7 × 6 + 3 {remainder ≠ 0, so 7 and 6 are not factors}

45/7 = 6 × 7 + 3 {remainder ≠ 0, so 6 and 7 are not factors}

We need to stop the division process because the numbers are repeated in multiplication.

Factors of 45 in Pair

When multiplying two numbers in a pair, we can find the pair factors of number 45, such as the following.

1 × 45 = 45

3 × 15 = 45

5 × 09 = 45

Thus, the pair factors are (1, 45), (3, 15), and (5, 9).

Prime Factorization of 45

In mathematics, 45 is a composite number. Let’s find its prime factorization now.

• The first step is to divide 45 by the smallest prime factor, which is 2.

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

• Let’s move on to the next prime number, which is 3.

• 45 ÷ 3 = 15
• 15 ÷ 3 = 5
• Again, dividing 5 by 3 gives us a fraction number, which cannot be a factor.

• Next, we’ll take a look at the number 5, which is the next prime number.
• 5 ÷ 5 = 1

• As we have received 1 at the end, we cannot proceed with the division method as ‘1’ does not have any multiples. Therefore, the prime factorization of 45 is 3 × 3 × 5 or 32 × 5, where 3 and 5 are prime numbers.

Solved Examples 

Example 1:

What are the common factors between 45 and 24?

Solution:

Factors of 45=1, 3, 5, 9, 15 and 45

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.

Hence, 45 and 24 have a common factor of 1.

Example 2:

Calculate the common factors of 45 and 50.

Solution:

1, 3, 5, 9, 15, and 45 are the factors of 45.

1, 2, 5, 10, 25, and 50 are the factors of 50.

Therefore, 45 and 50 have common factors 1 and 5.

Important key points:

Get Factors of more Numbers here:

FAQ’s