How to Find GCF of 78/48, 44/54, 871/76?

GCF of 78/48, 44/54, 871/76

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 78/48, 44/54, 871/76 i.e 1/8208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/48, 44/54, 871/76.

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 78/48,44/54,871/76?

Given fractions are 78/48,44/54,871/76

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 78/48,44/54,871/76, numerators are 78,44,871

Denominators are 48,54,76

The GCF of 78,44,871 is 1 .

LCM of 48,54,76 is 8208.

The greatest common factor of 78/48,44/54,871/76 = [GCF of 78,44,871]/[LCM of 48,54,76]= 1/8208

Therefore, the GCF of 78/48,44/54,871/76 is 1/8208.

Greatest Common Factor of 78,44,871

To find the highest common factor of 78,44,871, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 44 are 1, 2, 4, 11, 22, 44

The factors of 871 are 1, 13, 67, 871

The HCF of 78,44,871 is 1.

Lets's calculate GCF of 78,44,871

Greatest Common Factor (GCF) of 78,44,871 By Common Division

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

Greatest Common Factor of 78,44,871 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 44

1,2,4,11,22,44

Now, list down the factors of 871

1,13,67,871

Greatest Common Factor

We found the factors 78,44,871 . The biggest common factor number is the GCF number.
So the greatest common factor 78,44,871 is 1.

Lets's calculate LCM of 48,54,76

Lowest Common Multiple of 48,54,76 using Common Division

2	48, 54, 76
2	24, 27, 38
3	12, 27, 19
	4, 9, 19

∴ So the LCM of the given numbers is 2 x 2 x 3 x 4 x 9 x 19 = 8208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8208

Therefore, the GCF of Fractions 78/48,44/54,871/76 is 1/8208

Least Common Multiple of 48,54,76 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 48,54,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(48,54,76) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(48,54,76) x common factors =2 x 12 = 24

LCM(48,54,76) = ( 48 × 54 × 76 ) / 24

LCM(48,54,76) = 196992 / 24

LCM(48,54,76) = 8208

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FAQs on GCF of Fractions of 78/48, 44/54, 871/76

1. What is the HCF of 78,44,871?

The HCF of 78,44,871 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 78/48, 44/54, 871/76?

Answer: GCF of Numerators as per given numbers 78/48, 44/54, 871/76 is

GCF of Numerators i.e. for 78,44,871 is 1

LCM of denominators i.e. for 48,54,76 is 8208.

Thus, GCF of Fractions is 1/8208.Finally, GCF of Fractions for 78/48, 44/54, 871/76 is 1/8208.