How to Find GCF of 5797/424, 7688/2292?

GCF of 5797/424, 7688/2292

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 5797/424, 7688/2292 i.e 31/242952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5797/424, 7688/2292.

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 5797/424,7688/2292?

Given fractions are 5797/424,7688/2292

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 5797/424,7688/2292, numerators are 5797,7688

Denominators are 424,2292

The GCF of 5797,7688 is 31 .

LCM of 424,2292 is 242952.

The greatest common factor of 5797/424,7688/2292 = [GCF of 5797,7688]/[LCM of 424,2292]= 31/242952

Therefore, the GCF of 5797/424,7688/2292 is 31/242952.

Greatest Common Factor of 5797,7688

To find the highest common factor of 5797,7688, we have to find the factors of both numbers and list the highest common factor.

The factors of 5797 are 1, 11, 17, 31, 187, 341, 527, 5797

The factors of 7688 are 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, 7688

The HCF of 5797,7688 is 31.

Lets's calculate GCF of 5797,7688

Greatest Common Factor (GCF) of 5797,7688 By Common Division

31	5797, 7688
	187, 248

∴ So the GCF of the given numbers is 31 = 31

Greatest Common Factor of 5797,7688 By Matching Biggest Common Factor Method

Now, list down the factors of 5797

1,11,17,31,187,341,527,5797

Now, list down the factors of 7688

1,2,4,8,31,62,124,248,961,1922,3844,7688

Greatest Common Factor

We found the factors 5797,7688 . The biggest common factor number is the GCF number.
So the greatest common factor 5797,7688 is 31.

Lets's calculate LCM of 424,2292

Lowest Common Multiple of 424,2292 using Common Division

2	424, 2292
2	212, 1146
	106, 573

∴ So the LCM of the given numbers is 2 x 2 x 106 x 573 = 242952

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/242952

Therefore, the GCF of Fractions 5797/424,7688/2292 is 31/242952

Least Common Multiple of 424,2292 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 424,2292 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(424,2292) = 4

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

GCF(424,2292) x common factors =4 x 1 = 4

LCM(424,2292) = ( 424 × 2292 ) / 4

LCM(424,2292) = 971808 / 4

LCM(424,2292) = 242952

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FAQs on GCF of Fractions of 5797/424, 7688/2292

1. What is the HCF of 5797,7688?

The HCF of 5797,7688 is 31

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 5797/424, 7688/2292?

Answer: GCF of Numerators as per given numbers 5797/424, 7688/2292 is

GCF of Numerators i.e. for 5797,7688 is 31

LCM of denominators i.e. for 424,2292 is 242952.

Thus, GCF of Fractions is 31/242952.Finally, GCF of Fractions for 5797/424, 7688/2292 is 31/242952.