How to Find GCF of 78/200, 8502/6125?

GCF of 78/200, 8502/6125

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 78/200, 8502/6125 i.e 78/49000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/200, 8502/6125.

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 78/200,8502/6125?

Given fractions are 78/200,8502/6125

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 78/200,8502/6125, numerators are 78,8502

Denominators are 200,6125

The GCF of 78,8502 is 78 .

LCM of 200,6125 is 49000.

The greatest common factor of 78/200,8502/6125 = [GCF of 78,8502]/[LCM of 200,6125]= 78/49000

Therefore, the GCF of 78/200,8502/6125 is 78/49000.

Greatest Common Factor of 78,8502

To find the highest common factor of 78,8502, 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 8502 are 1, 2, 3, 6, 13, 26, 39, 78, 109, 218, 327, 654, 1417, 2834, 4251, 8502

The HCF of 78,8502 is 78.

Lets's calculate GCF of 78,8502

Greatest Common Factor (GCF) of 78,8502 By Common Division

2	78, 8502
3	39, 4251
13	13, 1417
	1, 109

∴ So the GCF of the given numbers is 2 x 3 x 13 = 78

Greatest Common Factor of 78,8502 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 8502

1,2,3,6,13,26,39,78,109,218,327,654,1417,2834,4251,8502

Greatest Common Factor

We found the factors 78,8502 . The biggest common factor number is the GCF number.
So the greatest common factor 78,8502 is 78.

Lets's calculate LCM of 200,6125

Lowest Common Multiple of 200,6125 using Common Division

5	200, 6125
5	40, 1225
	8, 245

∴ So the LCM of the given numbers is 5 x 5 x 8 x 245 = 49000

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 78/49000

Therefore, the GCF of Fractions 78/200,8502/6125 is 78/49000

Least Common Multiple of 200,6125 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 200,6125 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(200,6125) = 25

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

GCF(200,6125) x common factors =25 x 1 = 25

LCM(200,6125) = ( 200 × 6125 ) / 25

LCM(200,6125) = 1225000 / 25

LCM(200,6125) = 49000

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FAQs on GCF of Fractions of 78/200, 8502/6125

1. What is the HCF of 78,8502?

The HCF of 78,8502 is 78

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 78/200, 8502/6125?

Answer: GCF of Numerators as per given numbers 78/200, 8502/6125 is

GCF of Numerators i.e. for 78,8502 is 78

LCM of denominators i.e. for 200,6125 is 49000.

Thus, GCF of Fractions is 78/49000.Finally, GCF of Fractions for 78/200, 8502/6125 is 78/49000.