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GCF of 70 and 21

GCF of 70 and 21 is the largest possible number that divides 70 and 21 exactly without any remainder. The factors of 70 and 21 are 1, 2, 5, 7, 10, 14, 35, 70 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the GCF of 70 and 21 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 70 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 70 and 21?

Answer: GCF of 70 and 21 is 7.

Explanation:

The GCF of two non-zero integers, x(70) and y(21), is the greatest positive integer m(7) that divides both x(70) and y(21) without any remainder.

Methods to Find GCF of 70 and 21

The methods to find the GCF of 70 and 21 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 70 and 21 by Long Division

GCF of 70 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 70 (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 70 and 21.

GCF of 70 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 = 70 and Y = 21

GCF(70, 21) = GCF(21, 70 mod 21) = GCF(21, 7)
GCF(21, 7) = GCF(7, 21 mod 7) = GCF(7, 0)
GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 70 and 21 is 7.

GCF of 70 and 21 by Listing Common Factors

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 21: 1, 3, 7, 21

There are 2 common factors of 70 and 21, that are 1 and 7. Therefore, the greatest common factor of 70 and 21 is 7.

☛ Also Check:

GCF of 70 and 21 Examples

Example 1: For two numbers, GCF = 7 and LCM = 210. If one number is 70, find the other number.

Solution:

Given: GCF (z, 70) = 7 and LCM (z, 70) = 210
∵ GCF × LCM = 70 × (z)
⇒ z = (GCF × LCM)/70
⇒ z = (7 × 210)/70
⇒ z = 21
Therefore, the other number is 21.
Example 2: The product of two numbers is 1470. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 1470
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1470/7
Therefore, the LCM is 210.
Example 3: Find the GCF of 70 and 21, if their LCM is 210.

Solution:

∵ LCM × GCF = 70 × 21
⇒ GCF(70, 21) = (70 × 21)/210 = 7
Therefore, the greatest common factor of 70 and 21 is 7.

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FAQs on GCF of 70 and 21

What is the GCF of 70 and 21?

The GCF of 70 and 21 is 7. To calculate the greatest common factor (GCF) of 70 and 21, we need to factor each number (factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70; factors of 21 = 1, 3, 7, 21) and choose the greatest factor that exactly divides both 70 and 21, i.e., 7.

How to Find the GCF of 70 and 21 by Long Division Method?

To find the GCF of 70, 21 using long division method, 70 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 70, 21?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 70 and 21, i.e. GCF × LCM = 70 × 21.

What are the Methods to Find GCF of 70 and 21?

There are three commonly used methods to find the GCF of 70 and 21.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 70 and 21 by Prime Factorization?

To find the GCF of 70 and 21, we will find the prime factorization of the given numbers, i.e. 70 = 2 × 5 × 7; 21 = 3 × 7.
⇒ Since 7 is the only common prime factor of 70 and 21. Hence, GCF (70, 21) = 7.
☛ What is a Prime Number?

If the GCF of 21 and 70 is 7, Find its LCM.

GCF(21, 70) × LCM(21, 70) = 21 × 70
Since the GCF of 21 and 70 = 7
⇒ 7 × LCM(21, 70) = 1470
Therefore, LCM = 210
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