What is the GCF of 24 and 32?

To all the math learners, are you looking for specific answers to GCF of 24 and 32? This article can be highly beneficial for your school projects or homework. You will find precise answers to questions like, what is the product of the common prime factors of 24 and 32 and the least common multiple of 24 and 32? Read on to know more about the greatest common factor.

1. What do you call a Number with more than Two Factors?

Before we learn about the GCF of 24 and 32, let us look at what you call a number with more than two factors. A digit with more than two factors is called a composite number. You can check out the article on Prime and Composite numbers to know the details.

2. How do You find the Common Factors?

To find the common factor, follow the below instructions carefully.

There are two numbers: 24 and 40.

You need to break down the numbers. For 24, it will be,

• 24 = 4 × 6
• Now, you need to further break down the numbers to all the factors.
• 4 × 6 = 2 × 2 × 3 × 2.
• So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Now let’s find out the common factors of 40.

• 40 = 8 × 5
• (40 is written as) 8 × 5 = 2 × 2 × 2 × 5.
• So, the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

In this example, 2 × 2 × 2 = 8 is the greatest common factor and the common factors are 1, 2, 4, and 8. (See What is the Very Last Number in the World?)

3. What means GCF in Math?

If we need to understand the GCF of 24 and 32, we first need to understand the meaning. The greatest factor is the greatest common factor, or GCF, that divides both digits. Let’s say to get the GCF of 18 and 24, first, we need to list down its prime factors. 

18 = 2 × 3 × 3

and 24 = 2 × 2 × 2 × 3

18 and 24 share one 2 and one 3 commonly. We need to multiply them to get the Greatest Common Factor.

So 2 × 3 = 6 is the GCF of 18 and 24. Must see What is a mathematical sentence example?

4. How many Factors do 24 have?

1, 2, 3, 4, 6, 8, 12, and 24, are the 8 factors of digit 24.

5. What is the Highest Factor of 24?

The highest factor of 24 is 24 only as the factors are 1, 2, 3, 4, 6, 8, 12, and 24. (See How many Degrees in a Third of a Full Turn are there?)

6. What are the Factors of 32?

The factors of digit 32 are 1, 2, 4, 8, 16, and 32. (See Why is Mathematical Concept Important?)

7. What do 24 and 32 have in Common?

• 24 = 8 × 3,
• 8 × 3 = 2 × 2 × 2 × 3.
• 32 = 8 × 4,
• 8 × 4= 2 × 2 × 2 × 2 × 2.

Therefore, 2 × 2 × 2 or 8 is common between 24 and 32.

8. What is the GCF of 24 and 32?

The greatest common factor between 24 and 32 is 8.

9. What is the Product of the Common Prime Factors of 24 and 32?

The factors of  24 can be written as 24 = 2 × 2 × 2 × 3

The factors of  32 can be written as 32 = 2 × 2 × 2 × 2 × 2.

The common factor of 24 and 32 is 2 × 2 × 2 or 8.

So, 8 is the product of the common prime factors of 24 and 32. Must read How to find the Common Difference of the Arithmetic Sequence?

10. What is the Least Common Multiple of 24 and 32?

Now that we know what is the GCF of 24 and 32, let us find LCFs of the same. The least common multiple or LCM of digits 24 and 32 is 96.

To find the least common multiple of 24 and 32, you need to search the multiples of 24 and 32

• Multiples of 24 are 24, 48, 72, 96,…
• Multiples of 32 are 32, 64, 96, 128,… 
• Select the smallest multiple that is divisible by both 24 and 32, which is 96. 

11. What is the HCF of 18, 24 and 32?

To find out the HCF, you need positive integers that divide 18, 24, and 32, without a remainder.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of  24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 32 are 1, 2, 4, 8, 16, and 32.

The most common factor that has come up consistently is number 2. And it is also the HCF (Highest Common Factor) or GCF (Greatest Common Factor). (See How can You change 0.33 to a Fraction Accurately?)

12. What is the HCF of 24 and 32 by Prime Factor Method?

The prime factorization method for 24 and 36 is given below using the division method:

24 ÷ 2 = 12

12 ÷2 = 6

6 ÷ 2 = 3

Therefore, 24 = 2 × 2 × 2 × 3, are the factors.

32 ÷ 2  = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

Therefore, 32 = 2 × 2 × 2 × 2 × 2 , are the factors. Notice, the common set, i.e., 2 × 2 × 2 = 8

Therefore, the Highest Common Factor of 24 and 32 is 8. (See What is a circle in a degree chart?)

13. What are the Common Factors of 24 and 36?

What is the GCF of 24 and 32 is an answer we know, however, what is the common factor of 24 and 36?

• The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
• The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
• Common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12. 

I hope all the mathematical geeks and lovers or even the school kids enjoyed this article. Do share it across! (Also read When were numbers invented?)