Factors of 24 are the numbers that, when multiplied in pairs, give the product as 24. The factors can be both positive and negative. The number 24 is most significant as the number of hours in a day, but it also is an even composite number, which means that it has several factors. There are a total of 8 factors of 24. In this lesson, we will calculate the factors of 24, prime factors, and factors in pairs of 24 along with solved examples for a better grasp of the concept.

**Factors of 24:**1, 2, 3, 4, 6, 8, 12, and 24**Factors of -24:**-1, -2, -3, -4, -6, -12, and -24**Prime Factorization of 24:**24 = 2^{3}× 3

**Table of Contents**

- What are Factors of 24?
- Important Notes
- How to Calculate Factors of 24?
- Factors of 24 by Prime Factorization
- Factors of 24 in Pairs
- FAQs on Factors of 24
- Tips and Tricks
- Factors of 24 Solved Examples
- Interactive Questions

## What are Factors of 24?

Before we move ahead, let's recall a little about factors. A factor is a number that divides the given number without any remainder. Factors of 24 are pairs of those numbers whose products results in 24.

**Important Notes:**

- Factors of a number may be
**prime numbers**or**composite numbers**. - Factors are always
**whole numbers**. They are never fractions or decimals.

## How to Calculate the Factors of 24?

To calculate the factors of any number, here in this case 24, we need to find all the numbers that would divide 24 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 24 respectively. The number 1 and the number itself would always be a factor of the given number.

Let us check the division of 24 by its factors. We express 24 as a product of its **prime factors** in the prime factorization method and we divide 24 with its divisors in the division method. Let us see which numbers divide 24 exactly without a **remainder** in which case the divisors, as well as the **quotients**, are the factors of 24.

- 24/1 = 24; therefore, 1 and 24 are factors of 24
- 24/2 = 12; therefore, 2 is a factor of 24
- 24/3 = 8; therefore, 3 is a factor of 24
- 24/4 = 6; therefore, 4 is a factor of 24

Hence, the **factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24**. To understand the concept of finding factors by prime factorization better, let us take a few more examples.

- Factors of 224 - The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
- Factors of 243 - The factors of 243 are 1, 3, 9, 27, 81, 243
- Factors of 245 - The factors of 245 are 1, 5, 7, 35, 49, 245
- Factors of 21 - The factors of 21 are 1, 3, 7, 21
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 48 - The factors of 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

## Factors of 24 by Prime Factorization

Prime factorization means expressing a composite number as the product of its **prime factors**. Factors of 24 by prime factorization are given by using the following steps:

**Step 1:** Write the pair of factors, which on multiplication, gives the required number.

- 24 can be factored as a product of 4 and 6.

**Step 2:** Check each of the factors to see whether each one of them is prime or not.

- 4 is not a prime number and can be dissociated as a product of 2 by itself or as a square of 2.
- 6 is not a prime number and can be dissociated as a product of 2 and 3.

**Step 3:** As per the criteria,

- 24 can be written as 24 = 4 × 6 = 2 × 2 × 2 × 3
- It can also be written as 24 = 2
^{3}× 3

## Factors of 24 in Pairs

**Pair factors** are pairs of those numbers that, when multiplied, give the product as the required number. Here, the required number is 24. Let's try visualizing it using blocks.

**Factors of 24 in pairs can be written as:**

Factors |
Pair factors |

1 × 24 = 24 | 1, 24 |

2 × 12 = 24 | 2, 12 |

3 × 8 = 24 | 3, 8 |

4 × 6 = 24 | 4, 6 |

6 × 4 = 24 | 6, 4 |

8 × 3 = 24 | 8, 3 |

12 × 2 = 24 | 12, 2 |

24 × 1 = 24 | 24, 1 |

These factors given above are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

**Let's have a look at negative pair factors.**

Factors |
Pair factors |

-1 × -24 = 24 | -1, - 24 |

-2 × -12 = 24 | -2, - 12 |

-3 × -8 = 24 | -3, -8 |

-4 × -6 = 24 | - 4, - 6 |

-6 × -4 = 24 | -6, -4 |

-8 × -3 = 24 | -8, - 3 |

-12 × -2 = 24 | - 12, -2 |

-24 × -1 = 24 | -24, -1 |

## FAQs on Factors of 24

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

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

The common factors of 24 and 40 are 1, 2, 4, and 8.

### How many Factors of 64 are Also Factors of 24?

The factors of 64 are 1, 2, 4, 8, 16, 32, 64, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 which means that the factors of 64 that are also the factors of 24 are 1, 2, 4, 8.

### What is the Greatest Common Factor of 52 and 24?

The factors of 52 are 1, 2, 4, 13, 26, 52, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The common factors of 52 and 24 are 1, 2, 4.

Therefore, the greatest common factor of 52 and 24 is 4.

### What is the sum of all the Factors of 24?

1, 2, 3, 4, 6, 8, 12, 24 are the factors of 24. Sum of all factors of 24 = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60

### How Many Factors of 24 are Perfect Squares?

Perfect squares are numbers that can be expressed as a product of a square of a number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. 4 can be written as a square of 2, i.e., 4 = 2^{2,} and 1 can be written as a square of 1, i.e., 1 = 1^{2}

Hence, there are two factors (1 and 4) of 24 that are perfect squares.

**Tips and Tricks:**

- 1 is the smallest factor of every number.
- Every number has a minimum of two factors, i.e. 1 and the number itself.
- All even numbers always have 2 as one of their factors.
- All the numbers which end in 5, will always have 5 as one of their factors.
- All the numbers which end in 0, will always have 1, 2, 5, and 10 as their factors.

## Factors of 24 Solved Examples

**Example 1: **Henry has to determine which pair factor of 24 on addition gives 14, subtraction gives 10, and division gives one of the factors of 24 which belongs to another pair. Which pair factor do you think it is?

**Solution:**

Henry writes down the details given to him:

- Addition of pair factors = 14
- Subtraction of pair factors = 10

Division of pair factors = One factor belonging to another pair. The pair factor is (12, 2). This pair factor on addition gives 14, on subtraction gives 10, and on division gives 6, which is another factor of 24 and is a part of another pair factor.

Therefore, (12, 2) is the required pair factor.

**Example 2:** Jenny has an apple tree. She plucks 24 apples from the tree every day. She has to distribute it among her 4 friends. How many apples will each friend get?

**Solution:**

Jenny has to divide 24 apples among her 4 friends. This means each friend gets 24/4, which is 6 apples.

Therefore, each friend will get 6 apples every day.

## 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.**