GCF of 10 and 21
GCF of 10 and 21 is the largest possible number that divides 10 and 21 exactly without any remainder. The factors of 10 and 21 are 1, 2, 5, 10 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the GCF of 10 and 21  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 10 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 10 and 21?
Answer: GCF of 10 and 21 is 1.
Explanation:
The GCF of two nonzero integers, x(10) and y(21), is the greatest positive integer m(1) that divides both x(10) and y(21) without any remainder.
Methods to Find GCF of 10 and 21
Let's look at the different methods for finding the GCF of 10 and 21.
 Using Euclid's Algorithm
 Listing Common Factors
 Long Division Method
GCF of 10 and 21 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 10 and 21 is 1.
GCF of 10 and 21 by Listing Common Factors
 Factors of 10: 1, 2, 5, 10
 Factors of 21: 1, 3, 7, 21
Since, 1 is the only common factor between 10 and 21. The Greatest Common Factor of 10 and 21 is 1.
GCF of 10 and 21 by Long Division
GCF of 10 and 21 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 10 and 21.
☛ Also Check:
 GCF of 32 and 80 = 16
 GCF of 7 and 35 = 7
 GCF of 18 and 45 = 9
 GCF of 7 and 9 = 1
 GCF of 15 and 75 = 15
 GCF of 72 and 84 = 12
 GCF of 80 and 100 = 20
GCF of 10 and 21 Examples

Example 1: For two numbers, GCF = 1 and LCM = 210. If one number is 21, find the other number.
Solution:
Given: GCF (y, 21) = 1 and LCM (y, 21) = 210
∵ GCF × LCM = 21 × (y)
⇒ y = (GCF × LCM)/21
⇒ y = (1 × 210)/21
⇒ y = 10
Therefore, the other number is 10. 
Example 2: Find the GCF of 10 and 21, if their LCM is 210.
Solution:
∵ LCM × GCF = 10 × 21
⇒ GCF(10, 21) = (10 × 21)/210 = 1
Therefore, the greatest common factor of 10 and 21 is 1. 
Example 3: 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.
FAQs on GCF of 10 and 21
What is the GCF of 10 and 21?
The GCF of 10 and 21 is 1. To calculate the GCF (Greatest Common Factor) of 10 and 21, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 21 = 1, 3, 7, 21) and choose the greatest factor that exactly divides both 10 and 21, i.e., 1.
What are the Methods to Find GCF of 10 and 21?
There are three commonly used methods to find the GCF of 10 and 21.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
How to Find the GCF of 10 and 21 by Long Division Method?
To find the GCF of 10, 21 using long division method, 21 is divided by 10. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
If the GCF of 21 and 10 is 1, Find its LCM.
GCF(21, 10) × LCM(21, 10) = 21 × 10
Since the GCF of 21 and 10 = 1
⇒ 1 × LCM(21, 10) = 210
Therefore, LCM = 210
☛ GCF Calculator
How to Find the GCF of 10 and 21 by Prime Factorization?
To find the GCF of 10 and 21, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 21 = 3 × 7.
⇒ There is no common prime factor for 10 and 21. Hence, GCF (10, 21) = 1.
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 10, 21?
The following equation can be used to express the relation between LCM and GCF of 10 and 21, i.e. GCF × LCM = 10 × 21.
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