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GCF of 78/284, 7371/8458

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 78/284, 7371/8458 i.e 39/1201036 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/284, 7371/8458.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 78/284,7371/8458?

Given fractions are 78/284,7371/8458

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 78/284,7371/8458, numerators are 78,7371

Denominators are 284,8458

The GCF of 78,7371 is 39 .

LCM of 284,8458 is 1201036.

The greatest common factor of 78/284,7371/8458 = [GCF of 78,7371]/[LCM of 284,8458]= 39/1201036

Therefore, the GCF of 78/284,7371/8458 is 39/1201036.

Greatest Common Factor of 78,7371

To find the highest common factor of 78,7371, 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 7371 are 1, 3, 7, 9, 13, 21, 27, 39, 63, 81, 91, 117, 189, 273, 351, 567, 819, 1053, 2457, 7371

The HCF of 78,7371 is 39.

Lets's calculate GCF of 78,7371

Greatest Common Factor (GCF) of 78,7371 By Common Division

3 78, 7371
13 26, 2457
2, 189

∴ So the GCF of the given numbers is 3 x 13 = 39

Greatest Common Factor of 78,7371 By Matching Biggest Common Factor Method

Greatest Common Factor of 78,7371 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 7371

:

1,3,7,9,13,21,27,39,63,81,91,117,189,273,351,567,819,1053,2457,7371

Greatest Common Factor

We found the factors 78,7371 . The biggest common factor number is the GCF number.
So the greatest common factor 78,7371 is 39.


Lets's calculate LCM of 284,8458

Lowest Common Multiple of 284,8458 using Common Division

2 284, 8458
142, 4229

∴ So the LCM of the given numbers is 2 x 142 x 4229 = 1201036

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/1201036

Therefore, the GCF of Fractions 78/284,7371/8458 is 39/1201036

Least Common Multiple of 284,8458 with GCF Formula

Least Common Multiple of 284,8458 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 284,8458 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,8458) = 2

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

GCF(284,8458) x common factors =2 x 1 = 2

LCM(284,8458) = ( 284 × 8458 ) / 2

LCM(284,8458) = 2402072 / 2

LCM(284,8458) = 1201036


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 78/284, 7371/8458

1. What is the HCF of 78,7371?

The HCF of 78,7371 is 39

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 78/284, 7371/8458?

Answer: GCF of Numerators as per given numbers 78/284, 7371/8458 is

GCF of Numerators i.e. for 78,7371 is 39

LCM of denominators i.e. for 284,8458 is 1201036.

Thus, GCF of Fractions is 39/1201036.Finally, GCF of Fractions for 78/284, 7371/8458 is 39/1201036.