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GCF of 638/689, 109/287

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 638/689, 109/287 i.e 1/197743 easily. The following is the detailed procedure to determine the greatest common factor of fractions 638/689, 109/287.

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 638/689,109/287?

Given fractions are 638/689,109/287

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 638/689,109/287, numerators are 638,109

Denominators are 689,287

The GCF of 638,109 is 1 .

LCM of 689,287 is 197743.

The greatest common factor of 638/689,109/287 = [GCF of 638,109]/[LCM of 689,287]= 1/197743

Therefore, the GCF of 638/689,109/287 is 1/197743.

Greatest Common Factor of 638,109

To find the highest common factor of 638,109, we have to find the factors of both numbers and list the highest common factor.

The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638

The factors of 109 are 1, 109

The HCF of 638,109 is 1.

Lets's calculate GCF of 638,109

Greatest Common Factor (GCF) of 638,109 By Common Division

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

Greatest Common Factor of 638,109 By Matching Biggest Common Factor Method

Greatest Common Factor of 638,109 By Matching Biggest Common Factor Method

Now, list down the factors of 638

:

1,2,11,22,29,58,319,638

Now, list down the factors of 109

:

1,109

Greatest Common Factor

We found the factors 638,109 . The biggest common factor number is the GCF number.
So the greatest common factor 638,109 is 1.

Lets's calculate LCM of 689,287

Lowest Common Multiple of 689,287 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 197743

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/197743

Therefore, the GCF of Fractions 638/689,109/287 is 1/197743

Least Common Multiple of 689,287 with GCF Formula

Least Common Multiple of 689,287 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 689,287 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(689,287) = 1

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

GCF(689,287) x common factors =1 x 1 = 1

LCM(689,287) = ( 689 × 287 ) / 1

LCM(689,287) = 197743 / 1

LCM(689,287) = 197743


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FAQs on GCF of Fractions of 638/689, 109/287

1. What is the HCF of 638,109?

The HCF of 638,109 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 638/689, 109/287?

Answer: GCF of Numerators as per given numbers 638/689, 109/287 is

GCF of Numerators i.e. for 638,109 is 1

LCM of denominators i.e. for 689,287 is 197743.

Thus, GCF of Fractions is 1/197743.Finally, GCF of Fractions for 638/689, 109/287 is 1/197743.