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Factors Of 45

Factors of 45 are the numbers which when multiplied in pairs give the result as 45. For example, multiplication 2 and 3 gives 6, which means 2 and 3 are the factors of 6. Similarly, we can find all the factors 45. 

What are the Factors of 45?

Factors of 45 are the numbers, which divide the original number completely or uniformly. The numbers which give the result as 45 when multiplied together in pairs are the pair factors.

factors of 45

If we divide 84 with any of its factors, then the resulted quotient will be a whole number. 45, 36, 18, 60, 42, 30, 90, etc. are the composite numbers, which have more than 2 factors, unlike prime numbers.  To find the factors of a number and prime factors we can use the simple multiplication method and division method.

How to Find the Factors of 45?

In this section, you will learn the method of finding the factors of 45 by the division method. In this method, we should divide 45 by natural numbers 1, 2, 3, etc., and when we get the reminder 0, the corresponding divisor and quotient are treated as factors of 45.

Let us divide 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}

Here, the numbers are repeated in multiplication so we need to stop the division process.

Factors Of 45
1, 3, 5, 9, 15 and 45

Factors of 45 in Pair

We can find the pair factors of number 45, by multiplying two numbers in a pair to get the original number as 45, such as;

1 × 45 = 45

3 × 15 = 45

5 × 9 = 45

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

Prime Factorization of 45

The number 45 is a composite number. Now let us take out prime factorization of 45.

  • The first step is to divide the number 45 with the smallest prime factor, i.e. 2.

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

  • Now, proceed to the next prime numbers, i.e. 3.

45 ÷ 3 = 15

15 ÷ 3 = 5

  • Again, if we divide 5 by 3, we get a fraction number, which is not a factor.
  • Therefore, we will move to the next prime number, which is 5.

5 ÷ 5 = 1

  • We have received 1 at the end and further, we cannot proceed with the division method, as ‘1’ doesn’t have any multiples. So, the prime factorization of 45 is 3 × 3 × 5 or 32 × 5, where 3 and 5 are the prime numbers.

Video Lesson on Prime Factors

Go through the summary of factors of 45 given in the below table:

Factors of 45 1, 3, 5, 9, 15, 45
Negative factors of 45 -1, -3, -5, -9, -15, -45
Positive factor pairs of 45 (1, 45), (3, 15), (5, 9)
Negative factor pairs of 45 (-1, -45), (-3, -15), (-5, -9)
Prime factorization of 45 3 × 3 × 5 (Or) 32 × 5
Number of factors of 45 6
Sum of factors of 45 78

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Frequently Asked Questions on Factors of 45

What are the factors of 45 in maths?

The factors of 45 are 1, 3, 5, 9, 15 and 45. These factors can also be represented as:
1 × 45 = 45
3 × 15 = 45
5 × 9 = 45

What are the multiples of 45?

The first 10 multiples of 45 are 45, 90, 135, 180, 225, 270, 315, 360, 405, 450. Similarly, we can write an infinite number of multiples for 45.

Why is 45 not a prime number?

45 is not a prime number since it has more than two factors. As we know, a prime number has only two factors, 1 and the number itself.

What are the factors of 15 and 45?

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

Which number is a factor of 45 and a multiple of 3?

The numbers, which are the factors of 45 and multiple of 3, will be 9, 15, and 45.

Quiz on Factors of 45

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