How to Find GCF of 17/65, 438/91, 204/674?

GCF of 17/65, 438/91, 204/674

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 17/65, 438/91, 204/674 i.e 1/306670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/65, 438/91, 204/674.

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 17/65,438/91,204/674?

Given fractions are 17/65,438/91,204/674

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 17/65,438/91,204/674, numerators are 17,438,204

Denominators are 65,91,674

The GCF of 17,438,204 is 1 .

LCM of 65,91,674 is 306670.

The greatest common factor of 17/65,438/91,204/674 = [GCF of 17,438,204]/[LCM of 65,91,674]= 1/306670

Therefore, the GCF of 17/65,438/91,204/674 is 1/306670.

Greatest Common Factor of 17,438,204

To find the highest common factor of 17,438,204, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438

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

The HCF of 17,438,204 is 1.

Lets's calculate GCF of 17,438,204

Greatest Common Factor (GCF) of 17,438,204 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 17,438,204 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 438

1,2,3,6,73,146,219,438

Now, list down the factors of 204

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

Greatest Common Factor

We found the factors 17,438,204 . The biggest common factor number is the GCF number.
So the greatest common factor 17,438,204 is 1.

Lets's calculate LCM of 65,91,674

Lowest Common Multiple of 65,91,674 using Common Division

13	65, 91, 674
	5, 7, 674

∴ So the LCM of the given numbers is 13 x 5 x 7 x 674 = 306670

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/306670

Therefore, the GCF of Fractions 17/65,438/91,204/674 is 1/306670

Least Common Multiple of 65,91,674 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 65,91,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,91,674) = 1

common factors(in case of two or more numbers have common factors) = 13

GCF(65,91,674) x common factors =1 x 13 = 13

LCM(65,91,674) = ( 65 × 91 × 674 ) / 13

LCM(65,91,674) = 3986710 / 13

LCM(65,91,674) = 306670

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/65, 438/91, 204/674

1. What is the HCF of 17,438,204?

The HCF of 17,438,204 is 1

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 17/65, 438/91, 204/674?

Answer: GCF of Numerators as per given numbers 17/65, 438/91, 204/674 is

GCF of Numerators i.e. for 17,438,204 is 1

LCM of denominators i.e. for 65,91,674 is 306670.

Thus, GCF of Fractions is 1/306670.Finally, GCF of Fractions for 17/65, 438/91, 204/674 is 1/306670.