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GCF of 21 and 40

GCF of 21 and 40 is the largest possible number that divides 21 and 40 exactly without any remainder. The factors of 21 and 40 are 1, 3, 7, 21 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 21 and 40 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 21 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 40?

Answer: GCF of 21 and 40 is 1.

Explanation:

The GCF of two non-zero integers, x(21) and y(40), is the greatest positive integer m(1) that divides both x(21) and y(40) without any remainder.

Methods to Find GCF of 21 and 40

The methods to find the GCF of 21 and 40 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 21 and 40 by Prime Factorization

Prime factorization of 21 and 40 is (3 × 7) and (2 × 2 × 2 × 5) respectively. As visible, there are no common prime factors between 21 and 40, i.e. they are co-prime. Hence, the GCF of 21 and 40 will be 1.

GCF of 21 and 40 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

Since, 1 is the only common factor between 21 and 40. The Greatest Common Factor of 21 and 40 is 1.

GCF of 21 and 40 by Long Division

GCF of 21 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (19).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 21 and 40.

☛ Also Check:

GCF of 21 and 40 Examples

Example 1: Find the greatest number that divides 21 and 40 exactly.

Solution:

The greatest number that divides 21 and 40 exactly is their greatest common factor, i.e. GCF of 21 and 40.
⇒ Factors of 21 and 40:
- Factors of 21 = 1, 3, 7, 21
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 21 and 40 is 1.
Example 2: The product of two numbers is 840. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 840
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 840/1
Therefore, the LCM is 840.
Example 3: Find the GCF of 21 and 40, if their LCM is 840.

Solution:

∵ LCM × GCF = 21 × 40
⇒ GCF(21, 40) = (21 × 40)/840 = 1
Therefore, the greatest common factor of 21 and 40 is 1.

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FAQs on GCF of 21 and 40

What is the GCF of 21 and 40?

The GCF of 21 and 40 is 1. To calculate the GCF of 21 and 40, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 21 and 40, i.e., 1.

What are the Methods to Find GCF of 21 and 40?

There are three commonly used methods to find the GCF of 21 and 40.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 21 and 40 by Prime Factorization?

To find the GCF of 21 and 40, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 40 = 2 × 2 × 2 × 5.
⇒ There is no common prime factor for 21 and 40. Hence, GCF (21, 40) = 1.
☛ Prime Numbers

If the GCF of 40 and 21 is 1, Find its LCM.

GCF(40, 21) × LCM(40, 21) = 40 × 21
Since the GCF of 40 and 21 = 1
⇒ 1 × LCM(40, 21) = 840
Therefore, LCM = 840
☛ GCF Calculator

How to Find the GCF of 21 and 40 by Long Division Method?

To find the GCF of 21, 40 using long division method, 40 is divided by 21. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 21, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 21 and 40, i.e. GCF × LCM = 21 × 40.

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