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GCF of 137/22, 408/319

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 137/22, 408/319 i.e 1/638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 137/22, 408/319.

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 137/22,408/319?

Given fractions are 137/22,408/319

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 137/22,408/319, numerators are 137,408

Denominators are 22,319

The GCF of 137,408 is 1 .

LCM of 22,319 is 638.

The greatest common factor of 137/22,408/319 = [GCF of 137,408]/[LCM of 22,319]= 1/638

Therefore, the GCF of 137/22,408/319 is 1/638.

Greatest Common Factor of 137,408

To find the highest common factor of 137,408, we have to find the factors of both numbers and list the highest common factor.

The factors of 137 are 1, 137

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

The HCF of 137,408 is 1.

Lets's calculate GCF of 137,408

Greatest Common Factor (GCF) of 137,408 By Common Division

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

Greatest Common Factor of 137,408 By Matching Biggest Common Factor Method

Greatest Common Factor of 137,408 By Matching Biggest Common Factor Method

Now, list down the factors of 137

:

1,137

Now, list down the factors of 408

:

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Greatest Common Factor

We found the factors 137,408 . The biggest common factor number is the GCF number.
So the greatest common factor 137,408 is 1.

Lets's calculate LCM of 22,319

Lowest Common Multiple of 22,319 using Common Division

11 22, 319
2, 29

∴ So the LCM of the given numbers is 11 x 2 x 29 = 638

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/638

Therefore, the GCF of Fractions 137/22,408/319 is 1/638

Least Common Multiple of 22,319 with GCF Formula

Least Common Multiple of 22,319 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 22,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,319) = 11

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

GCF(22,319) x common factors =11 x 1 = 11

LCM(22,319) = ( 22 × 319 ) / 11

LCM(22,319) = 7018 / 11

LCM(22,319) = 638


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FAQs on GCF of Fractions of 137/22, 408/319

1. What is the HCF of 137,408?

The HCF of 137,408 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 137/22, 408/319?

Answer: GCF of Numerators as per given numbers 137/22, 408/319 is

GCF of Numerators i.e. for 137,408 is 1

LCM of denominators i.e. for 22,319 is 638.

Thus, GCF of Fractions is 1/638.Finally, GCF of Fractions for 137/22, 408/319 is 1/638.