# Factors of 45—with division and 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, we can find all the factors of 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, unlike prime factorization of 24

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

## What are Factors of -45?

When we multiply two numbers, and we get -45 as a product, that 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.

## FAQ’s

### What are the factors of 45 in maths?

Factors of 45 are 1, 3, 5, 9, 15 and 45. Factors of 45 are also known 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.

We can also write an infinite number of multiples of 45.

### Why is 45 not a prime number?

Since 45 has more than two factors, it is not a prime number. We know that a prime number has only two factors, 1 and the number itself.

### What are the factors of 15 and 45?

The factors of 15 = 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?

There will be 9, 15, and 45, which are factors of 45 and multiples of 3.