How to Find GCF of 77/296, 1908/7732?

GCF of 77/296, 1908/7732

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 77/296, 1908/7732 i.e 1/572168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/296, 1908/7732.

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 77/296,1908/7732?

Given fractions are 77/296,1908/7732

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 77/296,1908/7732, numerators are 77,1908

Denominators are 296,7732

The GCF of 77,1908 is 1 .

LCM of 296,7732 is 572168.

The greatest common factor of 77/296,1908/7732 = [GCF of 77,1908]/[LCM of 296,7732]= 1/572168

Therefore, the GCF of 77/296,1908/7732 is 1/572168.

Greatest Common Factor of 77,1908

To find the highest common factor of 77,1908, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 1908 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 53, 106, 159, 212, 318, 477, 636, 954, 1908

The HCF of 77,1908 is 1.

Lets's calculate GCF of 77,1908

Greatest Common Factor (GCF) of 77,1908 By Common Division

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

Greatest Common Factor of 77,1908 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 1908

1,2,3,4,6,9,12,18,36,53,106,159,212,318,477,636,954,1908

Greatest Common Factor

We found the factors 77,1908 . The biggest common factor number is the GCF number.
So the greatest common factor 77,1908 is 1.

Lets's calculate LCM of 296,7732

Lowest Common Multiple of 296,7732 using Common Division

2	296, 7732
2	148, 3866
	74, 1933

∴ So the LCM of the given numbers is 2 x 2 x 74 x 1933 = 572168

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/572168

Therefore, the GCF of Fractions 77/296,1908/7732 is 1/572168

Least Common Multiple of 296,7732 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 296,7732 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(296,7732) = 4

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

GCF(296,7732) x common factors =4 x 1 = 4

LCM(296,7732) = ( 296 × 7732 ) / 4

LCM(296,7732) = 2288672 / 4

LCM(296,7732) = 572168

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 77/296, 1908/7732

1. What is the HCF of 77,1908?

The HCF of 77,1908 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 77/296, 1908/7732?

Answer: GCF of Numerators as per given numbers 77/296, 1908/7732 is

GCF of Numerators i.e. for 77,1908 is 1

LCM of denominators i.e. for 296,7732 is 572168.

Thus, GCF of Fractions is 1/572168.Finally, GCF of Fractions for 77/296, 1908/7732 is 1/572168.