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GCF of 21 and 35

GCF of 21 and 35 is the largest possible number that divides 21 and 35 exactly without any remainder. The factors of 21 and 35 are 1, 3, 7, 21 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 21 and 35 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 21 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 35?

Answer: GCF of 21 and 35 is 7.

Explanation:

The GCF of two non-zero integers, x(21) and y(35), is the greatest positive integer m(7) that divides both x(21) and y(35) without any remainder.

Methods to Find GCF of 21 and 35

Let's look at the different methods for finding the GCF of 21 and 35.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 21 and 35 by Long Division

GCF of 21 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 21 and 35.

GCF of 21 and 35 by Prime Factorization

Prime factorization of 21 and 35 is (3 × 7) and (5 × 7) respectively. As visible, 21 and 35 have only one common prime factor i.e. 7. Hence, the GCF of 21 and 35 is 7.

GCF of 21 and 35 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 21 and 35, that are 1 and 7. Therefore, the greatest common factor of 21 and 35 is 7.

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GCF of 21 and 35 Examples

Example 1: The product of two numbers is 735. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 735
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 735/7
Therefore, the LCM is 105.
Example 2: For two numbers, GCF = 7 and LCM = 105. If one number is 21, find the other number.

Solution:

Given: GCF (x, 21) = 7 and LCM (x, 21) = 105
∵ GCF × LCM = 21 × (x)
⇒ x = (GCF × LCM)/21
⇒ x = (7 × 105)/21
⇒ x = 35
Therefore, the other number is 35.
Example 3: Find the GCF of 21 and 35, if their LCM is 105.

Solution:

∵ LCM × GCF = 21 × 35
⇒ GCF(21, 35) = (21 × 35)/105 = 7
Therefore, the greatest common factor of 21 and 35 is 7.

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FAQs on GCF of 21 and 35

What is the GCF of 21 and 35?

The GCF of 21 and 35 is 7. To calculate the greatest common factor (GCF) of 21 and 35, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 21 and 35, i.e., 7.

What are the Methods to Find GCF of 21 and 35?

There are three commonly used methods to find the GCF of 21 and 35.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 21 and 35 by Long Division Method?

To find the GCF of 21, 35 using long division method, 35 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, 35?

The following equation can be used to express the relation between Least Common Multiple and GCF of 21 and 35, i.e. GCF × LCM = 21 × 35.

If the GCF of 35 and 21 is 7, Find its LCM.

GCF(35, 21) × LCM(35, 21) = 35 × 21
Since the GCF of 35 and 21 = 7
⇒ 7 × LCM(35, 21) = 735
Therefore, LCM = 105
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How to Find the GCF of 21 and 35 by Prime Factorization?

To find the GCF of 21 and 35, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 35 = 5 × 7.
⇒ Since 7 is the only common prime factor of 21 and 35. Hence, GCF (21, 35) = 7.
☛ What are Prime Numbers?

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