How to Find GCF of 196/42, 227/96, 677/39?

GCF of 196/42, 227/96, 677/39

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 196/42, 227/96, 677/39 i.e 1/8736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/42, 227/96, 677/39.

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 196/42,227/96,677/39?

Given fractions are 196/42,227/96,677/39

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 196/42,227/96,677/39, numerators are 196,227,677

Denominators are 42,96,39

The GCF of 196,227,677 is 1 .

LCM of 42,96,39 is 8736.

The greatest common factor of 196/42,227/96,677/39 = [GCF of 196,227,677]/[LCM of 42,96,39]= 1/8736

Therefore, the GCF of 196/42,227/96,677/39 is 1/8736.

Greatest Common Factor of 196,227,677

To find the highest common factor of 196,227,677, 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 227 are 1, 227

The factors of 677 are 1, 677

The HCF of 196,227,677 is 1.

Lets's calculate GCF of 196,227,677

Greatest Common Factor (GCF) of 196,227,677 By Common Division

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

Greatest Common Factor of 196,227,677 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 227

1,227

Now, list down the factors of 677

1,677

Greatest Common Factor

We found the factors 196,227,677 . The biggest common factor number is the GCF number.
So the greatest common factor 196,227,677 is 1.

Lets's calculate LCM of 42,96,39

Lowest Common Multiple of 42,96,39 using Common Division

2	42, 96, 39
3	21, 48, 39
	7, 16, 13

∴ So the LCM of the given numbers is 2 x 3 x 7 x 16 x 13 = 8736

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8736

Therefore, the GCF of Fractions 196/42,227/96,677/39 is 1/8736

Least Common Multiple of 42,96,39 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 42,96,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,96,39) = 3

common factors(in case of two or more numbers have common factors) = 6

GCF(42,96,39) x common factors =3 x 6 = 18

LCM(42,96,39) = ( 42 × 96 × 39 ) / 18

LCM(42,96,39) = 157248 / 18

LCM(42,96,39) = 8736

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FAQs on GCF of Fractions of 196/42, 227/96, 677/39

1. What is the HCF of 196,227,677?

The HCF of 196,227,677 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 196/42, 227/96, 677/39?

Answer: GCF of Numerators as per given numbers 196/42, 227/96, 677/39 is

GCF of Numerators i.e. for 196,227,677 is 1

LCM of denominators i.e. for 42,96,39 is 8736.

Thus, GCF of Fractions is 1/8736.Finally, GCF of Fractions for 196/42, 227/96, 677/39 is 1/8736.