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GCF of 21 and 10

GCF of 21 and 10 is the largest possible number that divides 21 and 10 exactly without any remainder. The factors of 21 and 10 are 1, 3, 7, 21 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 21 and 10 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 21 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 10?

Answer: GCF of 21 and 10 is 1.

Explanation:

The GCF of two non-zero integers, x(21) and y(10), is the greatest positive integer m(1) that divides both x(21) and y(10) without any remainder.

Methods to Find GCF of 21 and 10

Let's look at the different methods for finding the GCF of 21 and 10.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 21 and 10 by Long Division

GCF of 21 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 21 and 10.

GCF of 21 and 10 by Prime Factorization

Prime factorization of 21 and 10 is (3 × 7) and (2 × 5) respectively. As visible, there are no common prime factors between 21 and 10, i.e. they are co-prime. Hence, the GCF of 21 and 10 will be 1.

GCF of 21 and 10 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 = 21 and Y = 10

GCF(21, 10) = GCF(10, 21 mod 10) = GCF(10, 1)
GCF(10, 1) = GCF(1, 10 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 21 and 10 is 1.

☛ Also Check:

GCF of 21 and 10 Examples

Example 1: Find the greatest number that divides 21 and 10 exactly.

Solution:

The greatest number that divides 21 and 10 exactly is their greatest common factor, i.e. GCF of 21 and 10.
⇒ Factors of 21 and 10:
- Factors of 21 = 1, 3, 7, 21
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 21 and 10 is 1.
Example 2: The product of two numbers is 210. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 210
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 210/1
Therefore, the LCM is 210.
Example 3: For two numbers, GCF = 1 and LCM = 210. If one number is 10, find the other number.

Solution:

Given: GCF (x, 10) = 1 and LCM (x, 10) = 210
∵ GCF × LCM = 10 × (x)
⇒ x = (GCF × LCM)/10
⇒ x = (1 × 210)/10
⇒ x = 21
Therefore, the other number is 21.

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FAQs on GCF of 21 and 10

What is the GCF of 21 and 10?

The GCF of 21 and 10 is 1. To calculate the GCF (Greatest Common Factor) of 21 and 10, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 21 and 10, i.e., 1.

How to Find the GCF of 21 and 10 by Prime Factorization?

To find the GCF of 21 and 10, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 10 = 2 × 5.
⇒ There is no common prime factor for 21 and 10. Hence, GCF (21, 10) = 1.
☛ Prime Number

What are the Methods to Find GCF of 21 and 10?

There are three commonly used methods to find the GCF of 21 and 10.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 10 and 21 is 1, Find its LCM.

GCF(10, 21) × LCM(10, 21) = 10 × 21
Since the GCF of 10 and 21 = 1
⇒ 1 × LCM(10, 21) = 210
Therefore, LCM = 210
☛ GCF Calculator

What is the Relation Between LCM and GCF of 21, 10?

The following equation can be used to express the relation between LCM and GCF of 21 and 10, i.e. GCF × LCM = 21 × 10.

How to Find the GCF of 21 and 10 by Long Division Method?

To find the GCF of 21, 10 using long division method, 21 is divided by 10. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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