Factors of 40 are the list of integers that can be evenly divided into 40. Factors of -40 are just factors with a negative sign. Did you know that forty is the only number in English that has all its letters in alphabetical order? In this lesson, we will calculate the factors of 40, its prime factors, its factors in pairs and we will end this lesson with some solved examples for better learning.

**Factors of 40:**1, 2, 4, 5, 8, 10, 20, and 40**Negative Factors of 40:**-1, -2, -4, -5, -8, -10, -20 and -40**Prime Factorization of 40:**40 = 2^{3}× 5

**Table of Contents**

- What Are the Factors of 40?
- How to Calculate Factors of 40?
- Factors of 40 by Prime Factorization
- Important Notes
- Factors of 40 in Pairs
- FAQs on Factors of 40
- Factors of 40 Solved Examples
- Challenging Questions
- Interactive Questions

## What are Factors of 40?

The number 40 is an even composite number. Since it is even, it will have 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors. Consider the number 13. It has only two factors, 1 and 13 which means that it is prime. Now, let's take the case of 48. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. There are more than two factors of 14. Hence it is composite. Therefore factors of 40 are all the integers that 40 can be divided into which are 1, 2, 4, 8, 10, 20, 40.

**Step 1:**Let's begin calculating the factors of 40, starting with the smallest whole number, i.e., 1.**Step 2:**Divide 40 with this number. Is the remainder 0?- Yes! So, we will get 40 ÷ 1 = 40, and the remainder is 0.

**Step 3:**The next whole number is 2. Now divide 40 with this number. 40 ÷ 2 = 20- Proceeding in a similar manner, we get 40 = 1× 40 = 2 × 20 = 4 ×10 = 5 × 8.

- Hence, the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

**Explore factors using illustrations and interactive examples.**

- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 140 - The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
- Factors of 400 - The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

## Factors of 40 by Prime Factorization

Prime factorization means expressing a composite number as the product of its prime factors. To get the prime factorization of 40, we divide it by its smallest prime factor, which is 2, 40 ÷ 2 = 20. Now, 20 is divided by its smallest prime factor and the quotient is obtained. This process goes on till we get the quotient as 1.

**The prime factorization of 40 is shown below:**

Now that we have done the prime factorization of 40, we can multiply it and get the other factors. Can you try to find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.

**Important Notes:**

- As 40 ends with the digit 0, it will have 5 and 10 as its factors. This holds true for any number that ends with the digit 0.
- 40 is a non-perfect square number. Thus, it will have an even number of factors. This property holds true for every non-perfect square number.

## Factors of 40 in Pairs

The pairs of numbers which give 40 when multiplied are known as factor pairs of 40. The following are the factors of 40 in pairs.

Factors | Pair Factor |

1 × 40 = 40 | (1,40) |

2 × 20= 40 | (2,20) |

4 × 10 = 40 | (4,10) |

5 × 8 = 40 | (5,8) |

8 × 5 = 40 | (8,5) |

10 × 4 = 40 | (10,4) |

20 × 2 = 40 | (20,2) |

40 × 1 = 40 | (40,1) |

- Observe in the table above, after 5 × 8, the factors start repeating. So, it is enough to find factors till (5,8)
- If we consider negative integers, then both the numbers in the pair factors will be negative. We know that - ve × - ve = +ve
- So, we can have factor pairs of 40 as (-1,-40) ; (-2,-20); (-4,-10); (-5,-8)

**Challenging Questions:**

- Are 0.4 and 100 factors of 40? Why do you think so?
- Are -5 and 8 factors of 40? Why do you think so?

## FAQs on Factors of 40

### What are the Multiples of 40?

A multiple is a product of a number with another number. The first 10 multiples of 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360, 400.

### What are the Prime Factors of 40?

The prime factors of 40 are 1, 2, and 5.

### What are the Factors of 24 and 40?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and secondly, the factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.

### What are the Common Factors of 40 and 48?

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Hence the common factors are 1, 2, 4, 8.

### What are the Common Factors of 40 and 60?

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Therefore, the common factors are 1, 2, 4, 5, 10, 20.

**Example 1:**Peter and Andrew both have rectangular papers with dimensions as shown below.

The length and breadth of the first rectangular paper are 8 inches and 5 inches, and the length and breadth of the second rectangular paper are 10 inches and 4 inches. They place the two rectangles one over another. Since the two shapes do not overlap, Peter said that they don't have the same area. However, Andrew does not agree with him. Can you find out who is correct?

**Solution:**

- Area of a rectangle = length × breadth
- For the first rectangle, Area = 8 × 5 = 40
- For the second rectangle, Area = 10 × 4 = 40

Hence, the two rectangles have equal areas and Andrew is correct.

**Example 2: **Jill has (-4) as one of the factors of 40. How will she get the other factor?

**Solution:** 40 = Factor 1 × Factor 2, so we can say that 40 = (-4) × Factor 2. Now, calculating for factor 2, Factor 2 = 40 ÷ (-4) = (-10).

Hence, the other factor is -10.

## 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.**