What are factors, factor pairs, prime factorization, and how to find them? In this blog post, you will learn everything about factors of 24. Once you know how to find factors of numbers, you can quickly solve questions and practice finding factors of all numbers with your private math tutor. Let’s start with the basic concept of the factor with quick tips.
What is a Factor?
Multiplying two integers gives a product. The integers we multiply are known as the factors of the product. 1 and the number itself always counts as factors.
For example
4 x 2 = 8
Here, 4 and 2 are the factors of 8.
Moreover, 1 and 8 are also the factors of 8.
Factors of 24
Keeping the definition of factors in mind, the factors of 24 are the numbers (positive or negative whole numbers) that are evenly divisible by the number 24.
How to find the factors of 24
Take numbers one by one and divide them by 24. If the remainder is 0 (zero), that means the divisor is the factor of 24.
Let’s get started:
- 24 ÷ 1 = 24
- 24 ÷ 2 = 12
- 24 ÷ 3 = 8
- 24 ÷ 4 = 6
- 24 ÷ 5 = 4.8 (not a factor)
- 24 ÷ 6 = 4
- 24 ÷ 7 = 3.4 (not a factor)
- 24 ÷ 8 = 3
- 24 ÷ 9 = 2.6 (not a factor)
- 24 ÷ 10 = 2.4 (not a factor)
- 24 ÷ 11 = 2.2 (not a factor)
- 24 ÷ 12 = 2
- 24 ÷ 13 = 1.8 (not a factor)
- 24 ÷ 24 = 1
Hence, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
What is Factor Pairs?
Pairs of a number multiplied together to give the original number are known as factor pairs. In other words, combinations of two factors that give the product of actual numbers are called factor pairs. There are both negative and positive factors of a number.
Factor Pairs of 24
Following are the combination of two factors or factor pairs, both positive and possible negative factor pairs of 24, that you must know about:
| Positive Factor Pairs | Negative Factor Pairs |
| 1 x 24 = 24 | -1 x -24 = 24 |
| 2 x 12 = 24 | -2 x -12 = 24 |
| 3 x 8 = 24 | -3 x -8 = 24 |
| 4 x 6 = 24 | -4 x -6 = 24 |
| 8 x 3 = 24 | -8 x -3 = 24 |
| 12 x 2 = 24 | -12 x -2 = 24 |
| 24 x 1 = 24 | -24 x -1 = 24 |
Thus, the pair factors are represented as
- Positive factor pairs: (1, 24), (2, 12), (3, 8), and (4, 6).
- Negative factor pairs: (-1, -24), (-2, -12), (-3, -8), and (-4, -6).
What is Prime Factorization?
Finding which prime numbers multiply together to give or make the original number is known as prime factorization. Sometimes numbers need to repeat to write the prime factors of a number. Also, every number is a prime number in prime factorization. You can find the prime factorization of both composite numbers and prime numbers.
Prime factorization of 24
The prime factorization of 24 is 2 x 2 x 2 x 3 or 23 x 3
Here, 2 and 3 are the prime numbers even when 24 itself is a composite number.
How to find the prime factorization of 24
24 is a composite number, and here are a few steps to find its prime factors:
- Divide 24 with the smallest prime factor first
(Smallest prime factor is 2)
24 ÷ 2 = 12 - Now, divide 12 by the smallest prime number, i.e., 2
12 ÷ 2 = 6 - Again, divide 6 by 2
6 ÷ 2 = 3 - Now, divide 3 by any other prime number that gives 0 remainder
3 ÷ 3 = 1 - With 1, we cannot proceed further division. Thus, here we are done with finding the prime factors of 24.
Note
- Positive integers having more than two factors are called composite numbers.
- Integers are divisible by two distinct integers; 1 and the number itself are called prime numbers.
Facts to Remember
- 1 is the factor of all integers.
- 2 is the factor of all even numbers.
- When the sum of the number’s digit is a multiple of 3, then it is divisible by 3 and has a factor of 3.
- Integers ending with 0 are easily divisible by 10 and will have 10 as their factor.
- A number is divisible by 11 if the sum of its odd-positioned digits subtracted from the sum of even-positioned digits is divisible by 11.
- An integer that ends with 0 or 5 must have a factor of 5.
- 4 is the factor if the last digits are divisible by 4 or end with 00.
- Factoring is the best way to simplify or solve algebraic expressions.
- A factor divides completely, without leaving any remainder.
- Prime factorization always includes prime numbers.
Examples of Factors of 24
Question:
Jack has 24 chocolate cookies in his lunch box. He has to distribute the cookies among his 8 friends. How can he do it?
Solution:
Number of cookies Jack has = 24
Number of his friends = 8
Each friend will get = 24/8 = 3
Hence, each of Jack’s friends will get 3 cookies.
Question:
Find the sum of factors of 24?
Solution:
As the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
So,
Sum of its factors= 1+2+3+4+6+8+12+24 = 60
Thus, 60 is the sum of factors of 24.
Question:
Find the common factors of 24 and 12?
Solution:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 12: 1, 2, 3, 4, 6, 12
Thus, 1, 2, 3, 4, 6, and 12 are the common factors in numbers 24 and 12.
Quick Tip to Find a Factor
To find a factor of any number, simply find out what numbers should be multiplied together to get that number.