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GCF of 60 and 60

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

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

What is GCF of 60 and 60?

Answer: GCF of 60 and 60 is 60.

Explanation:

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

Methods to Find GCF of 60 and 60

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

Long Division Method
Using Euclid's Algorithm
Listing Factors

GCF of 60 and 60 by Long Division

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

Step 1: Divide 60 by 60.
Step 2: Since the remainder = 0, the divisor (60) is the GCF of 60 and 60.

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

GCF of 60 and 60 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 60 and Y = 60

GCF(60, 60) = GCF(60, 60 mod 60) = GCF(60, 0)
GCF(60, 0) = 60 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 60 and 60 is 60.

GCF of 60 and 60 by Listing Factors

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

All the 12 factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 divide both numbers (60, 60) exactly without leaving any remainder. Therefore, the greatest common factor of 60 and 60 will be the greatest factor among the ones listed above, i.e. 60.

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GCF of 60 and 60 Examples

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

Solution:

∵ LCM × GCF = 60 × 60
⇒ GCF(60, 60) = (60 × 60)/60 = 60
Therefore, the greatest common factor of 60 and 60 is 60.
Example 2: Find the greatest number that divides 60 and 60 exactly.

Solution:

The greatest number that divides 60 and 60 exactly is their greatest common factor, i.e. GCF of 60 and 60.
⇒ Factors of 60 and 60:
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the greatest number that divides both the given numbers(60, 60) exactly is their GCF(60).
Example 3: The product of two numbers is 3600. If their GCF is 60, what is their LCM?

Solution:

Given: GCF = 60 and product of numbers = 3600
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3600/60
Therefore, the LCM is 60.

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FAQs on GCF of 60 and 60

What is the GCF of 60 and 60?

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

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

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

By Long Division
By Listing Factors
By Euclidean Algorithm

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

GCF(60, 60) × LCM(60, 60) = 60 × 60
Since the GCF of 60 and 60 = 60
⇒ 60 × LCM(60, 60) = 3600
Therefore, LCM = 60
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What is the Relation Between LCM and GCF of 60, 60?

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

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

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

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