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GCF of 10 and 14

GCF of 10 and 14 is the largest possible number that divides 10 and 14 exactly without any remainder. The factors of 10 and 14 are 1, 2, 5, 10 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 10 and 14 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 10 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 14?

Answer: GCF of 10 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(10) and y(14), is the greatest positive integer m(2) that divides both x(10) and y(14) without any remainder.

Methods to Find GCF of 10 and 14

The methods to find the GCF of 10 and 14 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 10 and 14 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 10 and 14, that are 1 and 2. Therefore, the greatest common factor of 10 and 14 is 2.

GCF of 10 and 14 by Prime Factorization

Prime factorization of 10 and 14 is (2 × 5) and (2 × 7) respectively. As visible, 10 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 10 and 14 is 2.

GCF of 10 and 14 by Long Division

GCF of 10 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 14 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 10 and 14.

☛ Also Check:

GCF of 10 and 14 Examples

Example 1: Find the GCF of 10 and 14, if their LCM is 70.

Solution:

∵ LCM × GCF = 10 × 14
⇒ GCF(10, 14) = (10 × 14)/70 = 2
Therefore, the greatest common factor of 10 and 14 is 2.
Example 2: Find the greatest number that divides 10 and 14 exactly.

Solution:

The greatest number that divides 10 and 14 exactly is their greatest common factor, i.e. GCF of 10 and 14.
⇒ Factors of 10 and 14:
- Factors of 10 = 1, 2, 5, 10
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 10 and 14 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 70. If one number is 14, find the other number.

Solution:

Given: GCF (y, 14) = 2 and LCM (y, 14) = 70
∵ GCF × LCM = 14 × (y)
⇒ y = (GCF × LCM)/14
⇒ y = (2 × 70)/14
⇒ y = 10
Therefore, the other number is 10.

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FAQs on GCF of 10 and 14

What is the GCF of 10 and 14?

The GCF of 10 and 14 is 2. To calculate the GCF (Greatest Common Factor) of 10 and 14, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 10 and 14, i.e., 2.

How to Find the GCF of 10 and 14 by Long Division Method?

To find the GCF of 10, 14 using long division method, 14 is divided by 10. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 10 and 14 by Prime Factorization?

To find the GCF of 10 and 14, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 10 and 14. Hence, GCF (10, 14) = 2.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 10, 14?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 10 and 14, i.e. GCF × LCM = 10 × 14.

If the GCF of 14 and 10 is 2, Find its LCM.

GCF(14, 10) × LCM(14, 10) = 14 × 10
Since the GCF of 14 and 10 = 2
⇒ 2 × LCM(14, 10) = 140
Therefore, LCM = 70
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 10 and 14?

There are three commonly used methods to find the GCF of 10 and 14.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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