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GCF of 21 and 49

GCF of 21 and 49 is the largest possible number that divides 21 and 49 exactly without any remainder. The factors of 21 and 49 are 1, 3, 7, 21 and 1, 7, 49 respectively. There are 3 commonly used methods to find the GCF of 21 and 49 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 21 and 49
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 49?

Answer: GCF of 21 and 49 is 7.

Explanation:

The GCF of two non-zero integers, x(21) and y(49), is the greatest positive integer m(7) that divides both x(21) and y(49) without any remainder.

Methods to Find GCF of 21 and 49

The methods to find the GCF of 21 and 49 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 21 and 49 by Long Division

GCF of 21 and 49 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 49 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 21 and 49.

GCF of 21 and 49 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 49: 1, 7, 49

There are 2 common factors of 21 and 49, that are 1 and 7. Therefore, the greatest common factor of 21 and 49 is 7.

GCF of 21 and 49 by Prime Factorization

Prime factorization of 21 and 49 is (3 × 7) and (7 × 7) respectively. As visible, 21 and 49 have only one common prime factor i.e. 7. Hence, the GCF of 21 and 49 is 7.

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GCF of 21 and 49 Examples

Example 1: Find the GCF of 21 and 49, if their LCM is 147.

Solution:

∵ LCM × GCF = 21 × 49
⇒ GCF(21, 49) = (21 × 49)/147 = 7
Therefore, the greatest common factor of 21 and 49 is 7.
Example 2: The product of two numbers is 1029. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 1029
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1029/7
Therefore, the LCM is 147.
Example 3: Find the greatest number that divides 21 and 49 exactly.

Solution:

The greatest number that divides 21 and 49 exactly is their greatest common factor, i.e. GCF of 21 and 49.
⇒ Factors of 21 and 49:
- Factors of 21 = 1, 3, 7, 21
- Factors of 49 = 1, 7, 49
Therefore, the GCF of 21 and 49 is 7.

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FAQs on GCF of 21 and 49

What is the GCF of 21 and 49?

The GCF of 21 and 49 is 7. To calculate the GCF of 21 and 49, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 49 = 1, 7, 49) and choose the greatest factor that exactly divides both 21 and 49, i.e., 7.

How to Find the GCF of 21 and 49 by Prime Factorization?

To find the GCF of 21 and 49, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 49 = 7 × 7.
⇒ Since 7 is the only common prime factor of 21 and 49. Hence, GCF (21, 49) = 7.
☛ Prime Numbers

What are the Methods to Find GCF of 21 and 49?

There are three commonly used methods to find the GCF of 21 and 49.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 21 and 49 by Long Division Method?

To find the GCF of 21, 49 using long division method, 49 is divided by 21. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 21, 49?

The following equation can be used to express the relation between Least Common Multiple and GCF of 21 and 49, i.e. GCF × LCM = 21 × 49.

If the GCF of 49 and 21 is 7, Find its LCM.

GCF(49, 21) × LCM(49, 21) = 49 × 21
Since the GCF of 49 and 21 = 7
⇒ 7 × LCM(49, 21) = 1029
Therefore, LCM = 147
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