How to Find GCF of 204/14, 690/7197?

GCF of 204/14, 690/7197

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 204/14, 690/7197 i.e 6/100758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/14, 690/7197.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 204/14,690/7197?

Given fractions are 204/14,690/7197

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 204/14,690/7197, numerators are 204,690

Denominators are 14,7197

The GCF of 204,690 is 6 .

LCM of 14,7197 is 100758.

The greatest common factor of 204/14,690/7197 = [GCF of 204,690]/[LCM of 14,7197]= 6/100758

Therefore, the GCF of 204/14,690/7197 is 6/100758.

Greatest Common Factor of 204,690

To find the highest common factor of 204,690, we have to find the factors of both numbers and list the highest common factor.

The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

The HCF of 204,690 is 6.

Lets's calculate GCF of 204,690

Greatest Common Factor (GCF) of 204,690 By Common Division

2	204, 690
3	102, 345
	34, 115

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 204,690 By Matching Biggest Common Factor Method

Now, list down the factors of 204

1,2,3,4,6,12,17,34,51,68,102,204

Now, list down the factors of 690

1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690

Greatest Common Factor

We found the factors 204,690 . The biggest common factor number is the GCF number.
So the greatest common factor 204,690 is 6.

Lets's calculate LCM of 14,7197

Lowest Common Multiple of 14,7197 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 100758

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/100758

Therefore, the GCF of Fractions 204/14,690/7197 is 6/100758

Least Common Multiple of 14,7197 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 14,7197 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,7197) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(14,7197) x common factors =1 x 1 = 1

LCM(14,7197) = ( 14 × 7197 ) / 1

LCM(14,7197) = 100758 / 1

LCM(14,7197) = 100758

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FAQs on GCF of Fractions of 204/14, 690/7197

1. What is the HCF of 204,690?

The HCF of 204,690 is 6

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 204/14, 690/7197?

Answer: GCF of Numerators as per given numbers 204/14, 690/7197 is

GCF of Numerators i.e. for 204,690 is 6

LCM of denominators i.e. for 14,7197 is 100758.

Thus, GCF of Fractions is 6/100758.Finally, GCF of Fractions for 204/14, 690/7197 is 6/100758.