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GCF of 210 and 90

GCF of 210 and 90 is the largest possible number that divides 210 and 90 exactly without any remainder. The factors of 210 and 90 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 210 and 90 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 210 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 210 and 90?

Answer: GCF of 210 and 90 is 30.

Explanation:

The GCF of two non-zero integers, x(210) and y(90), is the greatest positive integer m(30) that divides both x(210) and y(90) without any remainder.

Methods to Find GCF of 210 and 90

The methods to find the GCF of 210 and 90 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 210 and 90 by Long Division

GCF of 210 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 210 (larger number) by 90 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (90) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (30) is the GCF of 210 and 90.

GCF of 210 and 90 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 = 210 and Y = 90

GCF(210, 90) = GCF(90, 210 mod 90) = GCF(90, 30)
GCF(90, 30) = GCF(30, 90 mod 30) = GCF(30, 0)
GCF(30, 0) = 30 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 210 and 90 is 30.

GCF of 210 and 90 by Listing Common Factors

Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 8 common factors of 210 and 90, that are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor of 210 and 90 is 30.

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GCF of 210 and 90 Examples

Example 1: Find the GCF of 210 and 90, if their LCM is 630.

Solution:

∵ LCM × GCF = 210 × 90
⇒ GCF(210, 90) = (210 × 90)/630 = 30
Therefore, the greatest common factor of 210 and 90 is 30.
Example 2: For two numbers, GCF = 30 and LCM = 630. If one number is 210, find the other number.

Solution:

Given: GCF (x, 210) = 30 and LCM (x, 210) = 630
∵ GCF × LCM = 210 × (x)
⇒ x = (GCF × LCM)/210
⇒ x = (30 × 630)/210
⇒ x = 90
Therefore, the other number is 90.
Example 3: Find the greatest number that divides 210 and 90 exactly.

Solution:

The greatest number that divides 210 and 90 exactly is their greatest common factor, i.e. GCF of 210 and 90.
⇒ Factors of 210 and 90:
- Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 210 and 90 is 30.

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FAQs on GCF of 210 and 90

What is the GCF of 210 and 90?

The GCF of 210 and 90 is 30. To calculate the greatest common factor of 210 and 90, we need to factor each number (factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 210 and 90, i.e., 30.

If the GCF of 90 and 210 is 30, Find its LCM.

GCF(90, 210) × LCM(90, 210) = 90 × 210
Since the GCF of 90 and 210 = 30
⇒ 30 × LCM(90, 210) = 18900
Therefore, LCM = 630
☛ Greatest Common Factor Calculator

How to Find the GCF of 210 and 90 by Prime Factorization?

To find the GCF of 210 and 90, we will find the prime factorization of the given numbers, i.e. 210 = 2 × 3 × 5 × 7; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 210 and 90. Hence, GCF(210, 90) = 2 × 3 × 5 = 30
☛ Prime Numbers

How to Find the GCF of 210 and 90 by Long Division Method?

To find the GCF of 210, 90 using long division method, 210 is divided by 90. The corresponding divisor (30) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 210, 90?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 210 and 90, i.e. GCF × LCM = 210 × 90.

What are the Methods to Find GCF of 210 and 90?

There are three commonly used methods to find the GCF of 210 and 90.

By Listing Common Factors
By Long Division
By Prime Factorization

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