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GCF of 24 and 80

GCF of 24 and 80 is the largest possible number that divides 24 and 80 exactly without any remainder. The factors of 24 and 80 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 24 and 80 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 24 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 80?

Answer: GCF of 24 and 80 is 8.

Explanation:

The GCF of two non-zero integers, x(24) and y(80), is the greatest positive integer m(8) that divides both x(24) and y(80) without any remainder.

Methods to Find GCF of 24 and 80

The methods to find the GCF of 24 and 80 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 24 and 80 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

There are 4 common factors of 24 and 80, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 24 and 80 is 8.

GCF of 24 and 80 by Prime Factorization

Prime factorization of 24 and 80 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 24 and 80 have common prime factors. Hence, the GCF of 24 and 80 is 2 × 2 × 2 = 8.

GCF of 24 and 80 by Long Division

GCF of 24 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 80 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 24 and 80.

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GCF of 24 and 80 Examples

Example 1: The product of two numbers is 1920. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 1920
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1920/8
Therefore, the LCM is 240.
Example 2: Find the greatest number that divides 24 and 80 exactly.

Solution:

The greatest number that divides 24 and 80 exactly is their greatest common factor, i.e. GCF of 24 and 80.
⇒ Factors of 24 and 80:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Therefore, the GCF of 24 and 80 is 8.
Example 3: Find the GCF of 24 and 80, if their LCM is 240.

Solution:

∵ LCM × GCF = 24 × 80
⇒ GCF(24, 80) = (24 × 80)/240 = 8
Therefore, the greatest common factor of 24 and 80 is 8.

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FAQs on GCF of 24 and 80

What is the GCF of 24 and 80?

The GCF of 24 and 80 is 8. To calculate the greatest common factor (GCF) of 24 and 80, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 24 and 80, i.e., 8.

If the GCF of 80 and 24 is 8, Find its LCM.

GCF(80, 24) × LCM(80, 24) = 80 × 24
Since the GCF of 80 and 24 = 8
⇒ 8 × LCM(80, 24) = 1920
Therefore, LCM = 240
☛ Greatest Common Factor Calculator

How to Find the GCF of 24 and 80 by Long Division Method?

To find the GCF of 24, 80 using long division method, 80 is divided by 24. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

How to Find the GCF of 24 and 80 by Prime Factorization?

To find the GCF of 24 and 80, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 24 and 80. Hence, GCF(24, 80) = 2 × 2 × 2 = 8
☛ Prime Number

What are the Methods to Find GCF of 24 and 80?

There are three commonly used methods to find the GCF of 24 and 80.

By Long Division
By Euclidean Algorithm
By Prime Factorization

What is the Relation Between LCM and GCF of 24, 80?

The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 80, i.e. GCF × LCM = 24 × 80.

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