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GCF of 50 and 60

GCF of 50 and 60 is the largest possible number that divides 50 and 60 exactly without any remainder. The factors of 50 and 60 are 1, 2, 5, 10, 25, 50 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 50 and 60 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 50 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 50 and 60?

Answer: GCF of 50 and 60 is 10.

Explanation:

The GCF of two non-zero integers, x(50) and y(60), is the greatest positive integer m(10) that divides both x(50) and y(60) without any remainder.

Methods to Find GCF of 50 and 60

The methods to find the GCF of 50 and 60 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 50 and 60 by Prime Factorization

Prime factorization of 50 and 60 is (2 × 5 × 5) and (2 × 2 × 3 × 5) respectively. As visible, 50 and 60 have common prime factors. Hence, the GCF of 50 and 60 is 2 × 5 = 10.

GCF of 50 and 60 by Long Division

GCF of 50 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 50 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (50) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 50 and 60.

GCF of 50 and 60 by Listing Common Factors

Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 4 common factors of 50 and 60, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 50 and 60 is 10.

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GCF of 50 and 60 Examples

Example 1: Find the greatest number that divides 50 and 60 exactly.

Solution:

The greatest number that divides 50 and 60 exactly is their greatest common factor, i.e. GCF of 50 and 60.
⇒ Factors of 50 and 60:
- Factors of 50 = 1, 2, 5, 10, 25, 50
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the GCF of 50 and 60 is 10.
Example 2: For two numbers, GCF = 10 and LCM = 300. If one number is 50, find the other number.

Solution:

Given: GCF (x, 50) = 10 and LCM (x, 50) = 300
∵ GCF × LCM = 50 × (x)
⇒ x = (GCF × LCM)/50
⇒ x = (10 × 300)/50
⇒ x = 60
Therefore, the other number is 60.
Example 3: Find the GCF of 50 and 60, if their LCM is 300.

Solution:

∵ LCM × GCF = 50 × 60
⇒ GCF(50, 60) = (50 × 60)/300 = 10
Therefore, the greatest common factor of 50 and 60 is 10.

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FAQs on GCF of 50 and 60

What is the GCF of 50 and 60?

The GCF of 50 and 60 is 10. To calculate the greatest common factor of 50 and 60, we need to factor each number (factors of 50 = 1, 2, 5, 10, 25, 50; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 50 and 60, i.e., 10.

What is the Relation Between LCM and GCF of 50, 60?

The following equation can be used to express the relation between LCM and GCF of 50 and 60, i.e. GCF × LCM = 50 × 60.

If the GCF of 60 and 50 is 10, Find its LCM.

GCF(60, 50) × LCM(60, 50) = 60 × 50
Since the GCF of 60 and 50 = 10
⇒ 10 × LCM(60, 50) = 3000
Therefore, LCM = 300
☛ Greatest Common Factor Calculator

How to Find the GCF of 50 and 60 by Long Division Method?

To find the GCF of 50, 60 using long division method, 60 is divided by 50. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 50 and 60?

There are three commonly used methods to find the GCF of 50 and 60.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 50 and 60 by Prime Factorization?

To find the GCF of 50 and 60, we will find the prime factorization of the given numbers, i.e. 50 = 2 × 5 × 5; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 50 and 60. Hence, GCF(50, 60) = 2 × 5 = 10
☛ What is a Prime Number?

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