How to Find GCF of 936/419, 198/678?

GCF of 936/419, 198/678

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 936/419, 198/678 i.e 18/284082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 936/419, 198/678.

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 936/419,198/678?

Given fractions are 936/419,198/678

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 936/419,198/678, numerators are 936,198

Denominators are 419,678

The GCF of 936,198 is 18 .

LCM of 419,678 is 284082.

The greatest common factor of 936/419,198/678 = [GCF of 936,198]/[LCM of 419,678]= 18/284082

Therefore, the GCF of 936/419,198/678 is 18/284082.

Greatest Common Factor of 936,198

To find the highest common factor of 936,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 936 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 936,198 is 18.

Lets's calculate GCF of 936,198

Greatest Common Factor (GCF) of 936,198 By Common Division

2	936, 198
3	468, 99
3	156, 33
	52, 11

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 936,198 By Matching Biggest Common Factor Method

Now, list down the factors of 936

1,2,3,4,6,8,9,12,13,18,24,26,36,39,52,72,78,104,117,156,234,312,468,936

Now, list down the factors of 198

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 936,198 . The biggest common factor number is the GCF number.
So the greatest common factor 936,198 is 18.

Lets's calculate LCM of 419,678

Lowest Common Multiple of 419,678 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 284082

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/284082

Therefore, the GCF of Fractions 936/419,198/678 is 18/284082

Least Common Multiple of 419,678 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 419,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(419,678) = 1

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

GCF(419,678) x common factors =1 x 1 = 1

LCM(419,678) = ( 419 × 678 ) / 1

LCM(419,678) = 284082 / 1

LCM(419,678) = 284082

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FAQs on GCF of Fractions of 936/419, 198/678

1. What is the HCF of 936,198?

The HCF of 936,198 is 18

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 936/419, 198/678?

Answer: GCF of Numerators as per given numbers 936/419, 198/678 is

GCF of Numerators i.e. for 936,198 is 18

LCM of denominators i.e. for 419,678 is 284082.

Thus, GCF of Fractions is 18/284082.Finally, GCF of Fractions for 936/419, 198/678 is 18/284082.