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GCF of 205/377, 338/416

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 205/377, 338/416 i.e 1/12064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/377, 338/416.

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 205/377,338/416?

Given fractions are 205/377,338/416

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 205/377,338/416, numerators are 205,338

Denominators are 377,416

The GCF of 205,338 is 1 .

LCM of 377,416 is 12064.

The greatest common factor of 205/377,338/416 = [GCF of 205,338]/[LCM of 377,416]= 1/12064

Therefore, the GCF of 205/377,338/416 is 1/12064.

Greatest Common Factor of 205,338

To find the highest common factor of 205,338, we have to find the factors of both numbers and list the highest common factor.

The factors of 205 are 1, 5, 41, 205

The factors of 338 are 1, 2, 13, 26, 169, 338

The HCF of 205,338 is 1.

Lets's calculate GCF of 205,338

Greatest Common Factor (GCF) of 205,338 By Common Division

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

Greatest Common Factor of 205,338 By Matching Biggest Common Factor Method

Greatest Common Factor of 205,338 By Matching Biggest Common Factor Method

Now, list down the factors of 205

:

1,5,41,205

Now, list down the factors of 338

:

1,2,13,26,169,338

Greatest Common Factor

We found the factors 205,338 . The biggest common factor number is the GCF number.
So the greatest common factor 205,338 is 1.

Lets's calculate LCM of 377,416

Lowest Common Multiple of 377,416 using Common Division

13 377, 416
29, 32

∴ So the LCM of the given numbers is 13 x 29 x 32 = 12064

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12064

Therefore, the GCF of Fractions 205/377,338/416 is 1/12064

Least Common Multiple of 377,416 with GCF Formula

Least Common Multiple of 377,416 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 377,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(377,416) = 13

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

GCF(377,416) x common factors =13 x 1 = 13

LCM(377,416) = ( 377 × 416 ) / 13

LCM(377,416) = 156832 / 13

LCM(377,416) = 12064


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FAQs on GCF of Fractions of 205/377, 338/416

1. What is the HCF of 205,338?

The HCF of 205,338 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 205/377, 338/416?

Answer: GCF of Numerators as per given numbers 205/377, 338/416 is

GCF of Numerators i.e. for 205,338 is 1

LCM of denominators i.e. for 377,416 is 12064.

Thus, GCF of Fractions is 1/12064.Finally, GCF of Fractions for 205/377, 338/416 is 1/12064.