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GCF of 687/34, 377/469

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 687/34, 377/469 i.e 1/15946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 687/34, 377/469.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 687/34,377/469?

Given fractions are 687/34,377/469

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 687/34,377/469, numerators are 687,377

Denominators are 34,469

The GCF of 687,377 is 1 .

LCM of 34,469 is 15946.

The greatest common factor of 687/34,377/469 = [GCF of 687,377]/[LCM of 34,469]= 1/15946

Therefore, the GCF of 687/34,377/469 is 1/15946.

Greatest Common Factor of 687,377

To find the highest common factor of 687,377, we have to find the factors of both numbers and list the highest common factor.

The factors of 687 are 1, 3, 229, 687

The factors of 377 are 1, 13, 29, 377

The HCF of 687,377 is 1.

Lets's calculate GCF of 687,377

Greatest Common Factor (GCF) of 687,377 By Common Division

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

Greatest Common Factor of 687,377 By Matching Biggest Common Factor Method

Greatest Common Factor of 687,377 By Matching Biggest Common Factor Method

Now, list down the factors of 687

:

1,3,229,687

Now, list down the factors of 377

:

1,13,29,377

Greatest Common Factor

We found the factors 687,377 . The biggest common factor number is the GCF number.
So the greatest common factor 687,377 is 1.

Lets's calculate LCM of 34,469

Lowest Common Multiple of 34,469 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 15946

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15946

Therefore, the GCF of Fractions 687/34,377/469 is 1/15946

Least Common Multiple of 34,469 with GCF Formula

Least Common Multiple of 34,469 with GCF Formula

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

We need to calculate greatest common factor of 34,469 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,469) = 1

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

GCF(34,469) x common factors =1 x 1 = 1

LCM(34,469) = ( 34 × 469 ) / 1

LCM(34,469) = 15946 / 1

LCM(34,469) = 15946


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FAQs on GCF of Fractions of 687/34, 377/469

1. What is the HCF of 687,377?

The HCF of 687,377 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 687/34, 377/469?

Answer: GCF of Numerators as per given numbers 687/34, 377/469 is

GCF of Numerators i.e. for 687,377 is 1

LCM of denominators i.e. for 34,469 is 15946.

Thus, GCF of Fractions is 1/15946.Finally, GCF of Fractions for 687/34, 377/469 is 1/15946.