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GCF of 24 and 60

GCF of 24 and 60 is the largest possible number that divides 24 and 60 exactly without any remainder. The factors of 24 and 60 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 24 and 60 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 24 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 60?

Answer: GCF of 24 and 60 is 12.

Explanation:

The GCF of two non-zero integers, x(24) and y(60), is the greatest positive integer m(12) that divides both x(24) and y(60) without any remainder.

Methods to Find GCF of 24 and 60

Let's look at the different methods for finding the GCF of 24 and 60.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 24 and 60 by Long Division

GCF of 24 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 24 and 60.

GCF of 24 and 60 by Prime Factorization

Prime factorization of 24 and 60 is (2 × 2 × 2 × 3) and (2 × 2 × 3 × 5) respectively. As visible, 24 and 60 have common prime factors. Hence, the GCF of 24 and 60 is 2 × 2 × 3 = 12.

GCF of 24 and 60 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 6 common factors of 24 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 24 and 60 is 12.

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GCF of 24 and 60 Examples

Example 1: Find the GCF of 24 and 60, if their LCM is 120.

Solution:

∵ LCM × GCF = 24 × 60
⇒ GCF(24, 60) = (24 × 60)/120 = 12
Therefore, the greatest common factor of 24 and 60 is 12.
Example 2: For two numbers, GCF = 12 and LCM = 120. If one number is 60, find the other number.

Solution:

Given: GCF (y, 60) = 12 and LCM (y, 60) = 120
∵ GCF × LCM = 60 × (y)
⇒ y = (GCF × LCM)/60
⇒ y = (12 × 120)/60
⇒ y = 24
Therefore, the other number is 24.
Example 3: The product of two numbers is 1440. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 1440
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1440/12
Therefore, the LCM is 120.

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FAQs on GCF of 24 and 60

What is the GCF of 24 and 60?

The GCF of 24 and 60 is 12. To calculate the greatest common factor (GCF) of 24 and 60, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 24 and 60, i.e., 12.

How to Find the GCF of 24 and 60 by Long Division Method?

To find the GCF of 24, 60 using long division method, 60 is divided by 24. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 24 and 60?

There are three commonly used methods to find the GCF of 24 and 60.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 60 and 24 is 12, Find its LCM.

GCF(60, 24) × LCM(60, 24) = 60 × 24
Since the GCF of 60 and 24 = 12
⇒ 12 × LCM(60, 24) = 1440
Therefore, LCM = 120
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What is the Relation Between LCM and GCF of 24, 60?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 60, i.e. GCF × LCM = 24 × 60.

How to Find the GCF of 24 and 60 by Prime Factorization?

To find the GCF of 24 and 60, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 24 and 60. Hence, GCF(24, 60) = 2 × 2 × 3 = 12
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