Factors of 45 are the numbers that, when multiplied in pairs, give the product as 45. These factors can be both positive as well as negative. Did you know that a football match consists of 2 halves of 45 minutes each? In this lesson, we will calculate the factors of 45, its prime factors, and its factors in pairs which we will understand with some solved examples at the end of the lesson.

**Factors of 45:**1, 3, 5, 9, 15, and 45**Negative factors of 45:**-1, -3, -5, -9, -15, and -45**Prime Factorization of 45:**45 = 3^{2}× 5

**Table of Contents**

- What are Factors of 45?
- How to Calculate Factors of 45?
- Factors of 45 by Prime Factorization
- Factors of 45 in Pairs
- Important Notes
- FAQs on Factors of 45
- Factors of 45 Solved Examples
- Challenging Questions
- Interactive Questions

## What are Factors of 45?

Factors of a number n are the numbers that completely divide the number n. It means that if the remainder in n/a is zero, then a is the factor of n.

We are talking here about factors of the number 45. Let's first see the numbers that completely divide 45.

- 45 ÷ 3 = 15
- 45 ÷ 5 = 9
- 45 ÷ 45 = 1

The numbers that divide 45 completely are:

## How to Calculate the Factors of 45?

Factors of any number n can be calculated by many methods. One of the methods is dividing the number by the smallest of the factors. Factors of the number 45 can be calculated as follows:

**Step 1:**Write the two smallest factors of 45 (except 1).**Step 2:**The two smallest factors of 45 are 3 and 5.**Step 3:**Divide 45 by 3 and 5 i.e. 45 ÷ 3 = 15 and 45 ÷ 5 = 9**Step 4:**So, 3, 5, 9, and 15 are the factors of 45.**Step 5:**Repeat step 2 as long as we are getting new factors. For 45, these are the only factors.**Step 6:**Include 1 and the number itself to the factors.

Hence, the factors of 45 are **1, 3, 5, 9, 15, **and** 45**. Explore factors using illustrations and interactive examples:

- Factors of 175 - The factors of 175 are 1, 5, 7, 25, 35, 175
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 25 - The factors of 25 are 1, 5, 25
- Factors of 35 - The factors of 35 are 1, 5, 7, 35
- Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
- Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

## Factors of 45 by Prime Factorization

The prime factorization method to calculate factors of any number is one of the most important methods. Many students prefer using prime factorization while performing calculations. In the prime factorization method, we can only factorize a number into its prime factors.

### Prime Numbers

Prime numbers are the numbers that have only two factors, 1 and the number itself. Examples of prime numbers: 2, 3, 5, 7, 11, 13 and so on.

Prime factors of 45 are **45 = 3 × 3 × 5** . Let's write all the factors of 45 using prime factors:

**Step 1:**Take all the numbers once: 3, 5**Step 2:**Multiply each number with another number, once.- 3 × 3 = 9
- 3 × 5 = 15
- Factors obtained are 9 and 15.
**Step 3:**Write all the factors of the number.

**Factors of 45: 1, 3, 5, 9, 15, 45**

Now that we have done prime factorization of 45, we can multiply it and get the other factors. Can you try and find out if all the factors are covered or not? As you might have already guessed, for prime numbers, there are no other factors.

## Factors of 45 in Pairs

The pair of factors of a number n is the set of two numbers which, when multiplied together, give the number n.

Factors of 45 are: 1, 3, 5, 9, 15, 45. Factors of 45 in pair are: **(1, 45), (3, 15), (5, 9)**

- 1 × 45 = 45
- 3 × 15 = 45
- 5 × 9 = 45

Negative factor pairs of 45 are: (-1, -45), (-3, -15), (-5, -9)

- -1 × -45 = 45
- -3 × -15 = 45
- -5 × -9 = 45

**Important Notes:**

- All the factors of 45 are 1, 3, 5, 9, 15, and 45.
- Prime factorization of 45 is 45 = 3
^{2}× 5. - There are no factors of a number n between (n, n/2).
- Factors of 45 in pair are: (1, 45), (3, 15), (5, 9).

## FAQs on Factors of 45

### What are all Factors of 45?

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

### What are the Negative Pair Factors of 45?

Negative pair factors of 45 are (-1, -45), (-3, -15), (-5, -9).

### What is the Highest Common Factor (HCF) of 45 and 30?

- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 45: 1, 3, 5, 9, 15, 45

Common factors of 15 and 30 are 1, 3, 5, and 15, therefore, the HCF is 15.

### What are the Common Factors of 45 and 75?

Factors of 45 are 1, 3, 5, 9, 15, 45 and the factors of 75 are 1, 3, 5, 15, 25, 75.

Therefore, Common factors of 45 and 75 are 1, 3, 5, and 15.

### What are the Common Factors of 45 and 48?

- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Therefore, common factors of 45 and 48 are 1 and 3.

## Factors of 45 Solved Examples

**Example 1: **John wants to distribute 45 apples and 75 bananas to his friends. What is the maximum number of friends he should distribute the fruits too, so that everyone gets an equal number of apples and bananas?

**Solution:**

John has 45 apples and 75 bananas.

To find the maximum number of friends he needs to invite, we need to calculate the HCF of 45 and 75.

- 45 = 1 × 3 × 3 × 5
- 75 = 1 × 3 × 5 × 5

HCF of 45 and 75 = 3 × 5 = 15. Hence, John should invite 15 friends. Each friend will get 3 apples and 5 bananas.

**Example 2:** Find the prime factors of 45.

**Solution:**

We know that all the factors of 45 are 1, 3, 5, 9, 15, and 45. A prime number that is not a composite number is a prime factor.

Prime factorization of 45 = 1 × 3 × 3 × 5. Therefore, Prime factors of 45 are 1, 3, and 5.

**Challenging Questions:**

- Mathew has the number 675, and his friend Peter has the number 585. What are the common factors of these two numbers?

## Interactive Questions

**Here are a few activities for you to practice.**

**Select/Type your answer and click the "Check Answer" button to see the result.**