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GCF of 24 and 72

GCF of 24 and 72 is the largest possible number that divides 24 and 72 exactly without any remainder. The factors of 24 and 72 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 24 and 72 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 24 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 72?

Answer: GCF of 24 and 72 is 24.

Explanation:

The GCF of two non-zero integers, x(24) and y(72), is the greatest positive integer m(24) that divides both x(24) and y(72) without any remainder.

Methods to Find GCF of 24 and 72

Let's look at the different methods for finding the GCF of 24 and 72.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 24 and 72 by Prime Factorization

Prime factorization of 24 and 72 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 24 and 72 have common prime factors. Hence, the GCF of 24 and 72 is 2 × 2 × 2 × 3 = 24.

GCF of 24 and 72 by Long Division

GCF of 24 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 24 (smaller number).
Step 2: Since the remainder = 0, the divisor (24) is the GCF of 24 and 72.

The corresponding divisor (24) is the GCF of 24 and 72.

GCF of 24 and 72 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 8 common factors of 24 and 72, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 24 and 72 is 24.

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GCF of 24 and 72 Examples

Example 1: For two numbers, GCF = 24 and LCM = 72. If one number is 72, find the other number.

Solution:

Given: GCF (y, 72) = 24 and LCM (y, 72) = 72
∵ GCF × LCM = 72 × (y)
⇒ y = (GCF × LCM)/72
⇒ y = (24 × 72)/72
⇒ y = 24
Therefore, the other number is 24.
Example 2: The product of two numbers is 1728. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 1728
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1728/24
Therefore, the LCM is 72.
Example 3: Find the greatest number that divides 24 and 72 exactly.

Solution:

The greatest number that divides 24 and 72 exactly is their greatest common factor, i.e. GCF of 24 and 72.
⇒ Factors of 24 and 72:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 24 and 72 is 24.

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FAQs on GCF of 24 and 72

What is the GCF of 24 and 72?

The GCF of 24 and 72 is 24. To calculate the greatest common factor of 24 and 72, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 24 and 72, i.e., 24.

If the GCF of 72 and 24 is 24, Find its LCM.

GCF(72, 24) × LCM(72, 24) = 72 × 24
Since the GCF of 72 and 24 = 24
⇒ 24 × LCM(72, 24) = 1728
Therefore, LCM = 72
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How to Find the GCF of 24 and 72 by Prime Factorization?

To find the GCF of 24 and 72, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 24 and 72. Hence, GCF(24, 72) = 2 × 2 × 2 × 3 = 24
☛ Prime Numbers

How to Find the GCF of 24 and 72 by Long Division Method?

To find the GCF of 24, 72 using long division method, 72 is divided by 24. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 24 and 72?

There are three commonly used methods to find the GCF of 24 and 72.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 24, 72?

The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 72, i.e. GCF × LCM = 24 × 72.

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