How to Find GCF of 4991/280, 7119/384?

GCF of 4991/280, 7119/384

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 4991/280, 7119/384 i.e 7/13440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4991/280, 7119/384.

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 4991/280,7119/384?

Given fractions are 4991/280,7119/384

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 4991/280,7119/384, numerators are 4991,7119

Denominators are 280,384

The GCF of 4991,7119 is 7 .

LCM of 280,384 is 13440.

The greatest common factor of 4991/280,7119/384 = [GCF of 4991,7119]/[LCM of 280,384]= 7/13440

Therefore, the GCF of 4991/280,7119/384 is 7/13440.

Greatest Common Factor of 4991,7119

To find the highest common factor of 4991,7119, we have to find the factors of both numbers and list the highest common factor.

The factors of 4991 are 1, 7, 23, 31, 161, 217, 713, 4991

The factors of 7119 are 1, 3, 7, 9, 21, 63, 113, 339, 791, 1017, 2373, 7119

The HCF of 4991,7119 is 7.

Lets's calculate GCF of 4991,7119

Greatest Common Factor (GCF) of 4991,7119 By Common Division

7	4991, 7119
	713, 1017

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 4991,7119 By Matching Biggest Common Factor Method

Now, list down the factors of 4991

1,7,23,31,161,217,713,4991

Now, list down the factors of 7119

1,3,7,9,21,63,113,339,791,1017,2373,7119

Greatest Common Factor

We found the factors 4991,7119 . The biggest common factor number is the GCF number.
So the greatest common factor 4991,7119 is 7.

Lets's calculate LCM of 280,384

Lowest Common Multiple of 280,384 using Common Division

2	280, 384
2	140, 192
2	70, 96
	35, 48

∴ So the LCM of the given numbers is 2 x 2 x 2 x 35 x 48 = 13440

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/13440

Therefore, the GCF of Fractions 4991/280,7119/384 is 7/13440

Least Common Multiple of 280,384 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 280,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(280,384) = 8

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

GCF(280,384) x common factors =8 x 1 = 8

LCM(280,384) = ( 280 × 384 ) / 8

LCM(280,384) = 107520 / 8

LCM(280,384) = 13440

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FAQs on GCF of Fractions of 4991/280, 7119/384

1. What is the HCF of 4991,7119?

The HCF of 4991,7119 is 7

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 4991/280, 7119/384?

Answer: GCF of Numerators as per given numbers 4991/280, 7119/384 is

GCF of Numerators i.e. for 4991,7119 is 7

LCM of denominators i.e. for 280,384 is 13440.

Thus, GCF of Fractions is 7/13440.Finally, GCF of Fractions for 4991/280, 7119/384 is 7/13440.