How to Find GCF of 304/424, 8456/5300?

GCF of 304/424, 8456/5300

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 304/424, 8456/5300 i.e 8/10600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/424, 8456/5300.

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 304/424,8456/5300?

Given fractions are 304/424,8456/5300

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 304/424,8456/5300, numerators are 304,8456

Denominators are 424,5300

The GCF of 304,8456 is 8 .

LCM of 424,5300 is 10600.

The greatest common factor of 304/424,8456/5300 = [GCF of 304,8456]/[LCM of 424,5300]= 8/10600

Therefore, the GCF of 304/424,8456/5300 is 8/10600.

Greatest Common Factor of 304,8456

To find the highest common factor of 304,8456, we have to find the factors of both numbers and list the highest common factor.

The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304

The factors of 8456 are 1, 2, 4, 7, 8, 14, 28, 56, 151, 302, 604, 1057, 1208, 2114, 4228, 8456

The HCF of 304,8456 is 8.

Lets's calculate GCF of 304,8456

Greatest Common Factor (GCF) of 304,8456 By Common Division

2	304, 8456
2	152, 4228
2	76, 2114
	38, 1057

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 304,8456 By Matching Biggest Common Factor Method

Now, list down the factors of 304

1,2,4,8,16,19,38,76,152,304

Now, list down the factors of 8456

1,2,4,7,8,14,28,56,151,302,604,1057,1208,2114,4228,8456

Greatest Common Factor

We found the factors 304,8456 . The biggest common factor number is the GCF number.
So the greatest common factor 304,8456 is 8.

Lets's calculate LCM of 424,5300

Lowest Common Multiple of 424,5300 using Common Division

2	424, 5300
2	212, 2650
53	106, 1325
	2, 25

∴ So the LCM of the given numbers is 2 x 2 x 53 x 2 x 25 = 10600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/10600

Therefore, the GCF of Fractions 304/424,8456/5300 is 8/10600

Least Common Multiple of 424,5300 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 424,5300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(424,5300) = 212

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

GCF(424,5300) x common factors =212 x 1 = 212

LCM(424,5300) = ( 424 × 5300 ) / 212

LCM(424,5300) = 2247200 / 212

LCM(424,5300) = 10600

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FAQs on GCF of Fractions of 304/424, 8456/5300

1. What is the HCF of 304,8456?

The HCF of 304,8456 is 8

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 304/424, 8456/5300?

Answer: GCF of Numerators as per given numbers 304/424, 8456/5300 is

GCF of Numerators i.e. for 304,8456 is 8

LCM of denominators i.e. for 424,5300 is 10600.

Thus, GCF of Fractions is 8/10600.Finally, GCF of Fractions for 304/424, 8456/5300 is 8/10600.