In the realm of numbers, a fundamental concept is factoring. Factors of a number are whole numbers that, when multiplied together, yield that number. When it comes to the number 24, factors are the specific numbers that, when multiplied, equal 24.
24 is a positive integer with a total of 8 factors: 1, 2, 3, 4, 6, 8, 12 and 24.
In this post, we will learn how to find those factors of 24.
How to Factorize 24
To find the factors, divide 24 by all whole numbers starting with 1. Stop when the result is smaller than the number you are dividing by. Only results that include whole numbers are factors.
These are all the positive integer pairs that can be multiplied to give you the product of 24. So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Rules:
- Even numbers are always divisible by 2
- If a number ends in 0 or 5, it is divisible by 5
Factors of 24 in Pairs
Factor pairs are the two numbers that can be multiplied to make the product, 24. All factor pairs for 24 are as follows:
- 1 × 24 = 24
- 2 × 12 = 24
- 3 × 8 = 24
- 4 × 6 = 24
These positive factors are the most commonly accepted answer; however, there are also negative factors of 24.
The negative factors of 24 are: -1, -2, -3, -4, -6, -8, -12, -24
The negative factor pairs of 24 are:
- -1 × -24 = 24
- -2 × -12 = 24
- -3 × -8 = 24
- -4 × -6 = 24
Prime Factorization of 24
Now that we’ve determined the factors, let’s delve deeper and calculate the prime factorization of 24.
To understand prime factors, you must know about prime numbers. A prime number (2, 7, 11, 13, 19, etc.) is a number that is greater than 1 and cannot be divided into smaller numbers. (They can only be divided by 1 and the number itself.)
Prime factorization is when a product is broken down into all of its prime factors.
The prime factorization of 24 is:
- 2 x 2 x 2 x 3 = 24
To get this number, we start with the smallest prime factor that 24 is divisible by: 2.
- 24 ÷ 2 = 12 (12 is not a prime number)
- 12 ÷ 2 = 6 (6 is not a prime number)
- 6 ÷ 2 = 3 (3 is a prime number)
So, the prime factorization of 24 is 2 x 2 x 2 x 3.
It can also be written as exponents.
The prime factors of 24 are: 2 x 2 x 2 x 3 = 23 x 3 = 24
Common Factors of 24
The common factors of two (or more) numbers are the factors that the numbers have in common. For example:
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 14 are: 1, 2, 7, 14
Their common factors are: 1 and 2
The greatest common factor is the largest of the common factors. For 24 and 14, the GCF is 2.
- What is the greatest common factor of 16 and 24?
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 16 are: 1, 2, 4, 8, 16
The greatest common factor is: 8
- What is the greatest common factor of 24 and 40?
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The greatest common factor is: 8
- What is the greatest common factor of 24 and 36?
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The greatest common factor is: 12
- What is the greatest common factor of 24 and 32?
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 32 are: 1, 2, 4, 8, 16, 32
The greatest common factor is: 8
- What is the greatest common factor of 18 and 24?
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 18 are: 1, 2, 3, 6, 9, 18
The greatest common factor is: 6
Related:
What are the factors of 18?