How to Find GCF of 5300/656, 5125/6679?

GCF of 5300/656, 5125/6679

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 5300/656, 5125/6679 i.e 25/4381424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5300/656, 5125/6679.

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 5300/656,5125/6679?

Given fractions are 5300/656,5125/6679

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 5300/656,5125/6679, numerators are 5300,5125

Denominators are 656,6679

The GCF of 5300,5125 is 25 .

LCM of 656,6679 is 4381424.

The greatest common factor of 5300/656,5125/6679 = [GCF of 5300,5125]/[LCM of 656,6679]= 25/4381424

Therefore, the GCF of 5300/656,5125/6679 is 25/4381424.

Greatest Common Factor of 5300,5125

To find the highest common factor of 5300,5125, we have to find the factors of both numbers and list the highest common factor.

The factors of 5300 are 1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650, 5300

The factors of 5125 are 1, 5, 25, 41, 125, 205, 1025, 5125

The HCF of 5300,5125 is 25.

Lets's calculate GCF of 5300,5125

Greatest Common Factor (GCF) of 5300,5125 By Common Division

5	5300, 5125
5	1060, 1025
	212, 205

∴ So the GCF of the given numbers is 5 x 5 = 25

Greatest Common Factor of 5300,5125 By Matching Biggest Common Factor Method

Now, list down the factors of 5300

1,2,4,5,10,20,25,50,53,100,106,212,265,530,1060,1325,2650,5300

Now, list down the factors of 5125

1,5,25,41,125,205,1025,5125

Greatest Common Factor

We found the factors 5300,5125 . The biggest common factor number is the GCF number.
So the greatest common factor 5300,5125 is 25.

Lets's calculate LCM of 656,6679

Lowest Common Multiple of 656,6679 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4381424

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/4381424

Therefore, the GCF of Fractions 5300/656,5125/6679 is 25/4381424

Least Common Multiple of 656,6679 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 656,6679 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(656,6679) = 1

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

GCF(656,6679) x common factors =1 x 1 = 1

LCM(656,6679) = ( 656 × 6679 ) / 1

LCM(656,6679) = 4381424 / 1

LCM(656,6679) = 4381424

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 5300/656, 5125/6679

1. What is the HCF of 5300,5125?

The HCF of 5300,5125 is 25

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 5300/656, 5125/6679?

Answer: GCF of Numerators as per given numbers 5300/656, 5125/6679 is

GCF of Numerators i.e. for 5300,5125 is 25

LCM of denominators i.e. for 656,6679 is 4381424.

Thus, GCF of Fractions is 25/4381424.Finally, GCF of Fractions for 5300/656, 5125/6679 is 25/4381424.