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GCF of 10 and 60

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

1.	GCF of 10 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 60?

Answer: GCF of 10 and 60 is 10.

Explanation:

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

Methods to Find GCF of 10 and 60

The methods to find the GCF of 10 and 60 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 10 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 = 10

GCF(60, 10) = GCF(10, 60 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 60 is 10.

GCF of 10 and 60 by Long Division

GCF of 10 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 10 (smaller number).
Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 60.

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

GCF of 10 and 60 by Prime Factorization

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

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GCF of 10 and 60 Examples

Example 1: The product of two numbers is 600. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 600
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 600/10
Therefore, the LCM is 60.
Example 2: Find the greatest number that divides 10 and 60 exactly.

Solution:

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

Solution:

Given: GCF (x, 60) = 10 and LCM (x, 60) = 60
∵ GCF × LCM = 60 × (x)
⇒ x = (GCF × LCM)/60
⇒ x = (10 × 60)/60
⇒ x = 10
Therefore, the other number is 10.

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FAQs on GCF of 10 and 60

What is the GCF of 10 and 60?

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

How to Find the GCF of 10 and 60 by Prime Factorization?

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

What are the Methods to Find GCF of 10 and 60?

There are three commonly used methods to find the GCF of 10 and 60.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 10, 60?

The following equation can be used to express the relation between LCM and GCF of 10 and 60, i.e. GCF × LCM = 10 × 60.

How to Find the GCF of 10 and 60 by Long Division Method?

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

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

GCF(60, 10) × LCM(60, 10) = 60 × 10
Since the GCF of 60 and 10 = 10
⇒ 10 × LCM(60, 10) = 600
Therefore, LCM = 60
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