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GCF of 196/268, 854/236

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 196/268, 854/236 i.e 14/15812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/268, 854/236.

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 196/268,854/236?

Given fractions are 196/268,854/236

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 196/268,854/236, numerators are 196,854

Denominators are 268,236

The GCF of 196,854 is 14 .

LCM of 268,236 is 15812.

The greatest common factor of 196/268,854/236 = [GCF of 196,854]/[LCM of 268,236]= 14/15812

Therefore, the GCF of 196/268,854/236 is 14/15812.

Greatest Common Factor of 196,854

To find the highest common factor of 196,854, we have to find the factors of both numbers and list the highest common factor.

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854

The HCF of 196,854 is 14.

Lets's calculate GCF of 196,854

Greatest Common Factor (GCF) of 196,854 By Common Division

2 196, 854
7 98, 427
14, 61

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 196,854 By Matching Biggest Common Factor Method

Greatest Common Factor of 196,854 By Matching Biggest Common Factor Method

Now, list down the factors of 196

:

1,2,4,7,14,28,49,98,196

Now, list down the factors of 854

:

1,2,7,14,61,122,427,854

Greatest Common Factor

We found the factors 196,854 . The biggest common factor number is the GCF number.
So the greatest common factor 196,854 is 14.

Lets's calculate LCM of 268,236

Lowest Common Multiple of 268,236 using Common Division

2 268, 236
2 134, 118
67, 59

∴ So the LCM of the given numbers is 2 x 2 x 67 x 59 = 15812

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/15812

Therefore, the GCF of Fractions 196/268,854/236 is 14/15812

Least Common Multiple of 268,236 with GCF Formula

Least Common Multiple of 268,236 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 268,236 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,236) = 4

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

GCF(268,236) x common factors =4 x 1 = 4

LCM(268,236) = ( 268 × 236 ) / 4

LCM(268,236) = 63248 / 4

LCM(268,236) = 15812


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FAQs on GCF of Fractions of 196/268, 854/236

1. What is the HCF of 196,854?

The HCF of 196,854 is 14

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 196/268, 854/236?

Answer: GCF of Numerators as per given numbers 196/268, 854/236 is

GCF of Numerators i.e. for 196,854 is 14

LCM of denominators i.e. for 268,236 is 15812.

Thus, GCF of Fractions is 14/15812.Finally, GCF of Fractions for 196/268, 854/236 is 14/15812.