How to Find GCF of 14/680, 18/975, 137/909?

GCF of 14/680, 18/975, 137/909

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 14/680, 18/975, 137/909 i.e 1/40177800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/680, 18/975, 137/909.

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 14/680,18/975,137/909?

Given fractions are 14/680,18/975,137/909

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 14/680,18/975,137/909, numerators are 14,18,137

Denominators are 680,975,909

The GCF of 14,18,137 is 1 .

LCM of 680,975,909 is 40177800.

The greatest common factor of 14/680,18/975,137/909 = [GCF of 14,18,137]/[LCM of 680,975,909]= 1/40177800

Therefore, the GCF of 14/680,18/975,137/909 is 1/40177800.

Greatest Common Factor of 14,18,137

To find the highest common factor of 14,18,137, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 18 are 1, 2, 3, 6, 9, 18

The factors of 137 are 1, 137

The HCF of 14,18,137 is 1.

Lets's calculate GCF of 14,18,137

Greatest Common Factor (GCF) of 14,18,137 By Common Division

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

Greatest Common Factor of 14,18,137 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 18

1,2,3,6,9,18

Now, list down the factors of 137

1,137

Greatest Common Factor

We found the factors 14,18,137 . The biggest common factor number is the GCF number.
So the greatest common factor 14,18,137 is 1.

Lets's calculate LCM of 680,975,909

Lowest Common Multiple of 680,975,909 using Common Division

3	680, 975, 909
5	680, 325, 303
	136, 65, 303

∴ So the LCM of the given numbers is 3 x 5 x 136 x 65 x 303 = 40177800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40177800

Therefore, the GCF of Fractions 14/680,18/975,137/909 is 1/40177800

Least Common Multiple of 680,975,909 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 680,975,909 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(680,975,909) = 1

common factors(in case of two or more numbers have common factors) = 15

GCF(680,975,909) x common factors =1 x 15 = 15

LCM(680,975,909) = ( 680 × 975 × 909 ) / 15

LCM(680,975,909) = 602667000 / 15

LCM(680,975,909) = 40177800

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/680, 18/975, 137/909

1. What is the HCF of 14,18,137?

The HCF of 14,18,137 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 14/680, 18/975, 137/909?

Answer: GCF of Numerators as per given numbers 14/680, 18/975, 137/909 is

GCF of Numerators i.e. for 14,18,137 is 1

LCM of denominators i.e. for 680,975,909 is 40177800.

Thus, GCF of Fractions is 1/40177800.Finally, GCF of Fractions for 14/680, 18/975, 137/909 is 1/40177800.