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GCF of 10 and 12

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

1.	GCF of 10 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 12?

Answer: GCF of 10 and 12 is 2.

Explanation:

The GCF of two non-zero integers, x(10) and y(12), is the greatest positive integer m(2) that divides both x(10) and y(12) without any remainder.

Methods to Find GCF of 10 and 12

The methods to find the GCF of 10 and 12 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 10 and 12 by Prime Factorization

Prime factorization of 10 and 12 is (2 × 5) and (2 × 2 × 3) respectively. As visible, 10 and 12 have only one common prime factor i.e. 2. Hence, the GCF of 10 and 12 is 2.

GCF of 10 and 12 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 12: 1, 2, 3, 4, 6, 12

There are 2 common factors of 10 and 12, that are 1 and 2. Therefore, the greatest common factor of 10 and 12 is 2.

GCF of 10 and 12 by Long Division

GCF of 10 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 10 and 12.

☛ Also Check:

GCF of 10 and 12 Examples

Example 1: Find the greatest number that divides 10 and 12 exactly.

Solution:

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

Solution:

Given: GCF (y, 10) = 2 and LCM (y, 10) = 60
∵ GCF × LCM = 10 × (y)
⇒ y = (GCF × LCM)/10
⇒ y = (2 × 60)/10
⇒ y = 12
Therefore, the other number is 12.
Example 3: The product of two numbers is 120. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 120
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 120/2
Therefore, the LCM is 60.

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FAQs on GCF of 10 and 12

What is the GCF of 10 and 12?

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

How to Find the GCF of 10 and 12 by Long Division Method?

To find the GCF of 10, 12 using long division method, 12 is divided by 10. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 10, 12?

The following equation can be used to express the relation between Least Common Multiple and GCF of 10 and 12, i.e. GCF × LCM = 10 × 12.

How to Find the GCF of 10 and 12 by Prime Factorization?

To find the GCF of 10 and 12, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 12 = 2 × 2 × 3.
⇒ Since 2 is the only common prime factor of 10 and 12. Hence, GCF (10, 12) = 2.
☛ What is a Prime Number?

If the GCF of 12 and 10 is 2, Find its LCM.

GCF(12, 10) × LCM(12, 10) = 12 × 10
Since the GCF of 12 and 10 = 2
⇒ 2 × LCM(12, 10) = 120
Therefore, LCM = 60
☛ GCF Calculator

What are the Methods to Find GCF of 10 and 12?

There are three commonly used methods to find the GCF of 10 and 12.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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