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GCF of 975/197, 689/936

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 975/197, 689/936 i.e 13/184392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/197, 689/936.

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 975/197,689/936?

Given fractions are 975/197,689/936

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 975/197,689/936, numerators are 975,689

Denominators are 197,936

The GCF of 975,689 is 13 .

LCM of 197,936 is 184392.

The greatest common factor of 975/197,689/936 = [GCF of 975,689]/[LCM of 197,936]= 13/184392

Therefore, the GCF of 975/197,689/936 is 13/184392.

Greatest Common Factor of 975,689

To find the highest common factor of 975,689, we have to find the factors of both numbers and list the highest common factor.

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975

The factors of 689 are 1, 13, 53, 689

The HCF of 975,689 is 13.

Lets's calculate GCF of 975,689

Greatest Common Factor (GCF) of 975,689 By Common Division

13 975, 689
75, 53

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 975,689 By Matching Biggest Common Factor Method

Greatest Common Factor of 975,689 By Matching Biggest Common Factor Method

Now, list down the factors of 975

:

1,3,5,13,15,25,39,65,75,195,325,975

Now, list down the factors of 689

:

1,13,53,689

Greatest Common Factor

We found the factors 975,689 . The biggest common factor number is the GCF number.
So the greatest common factor 975,689 is 13.

Lets's calculate LCM of 197,936

Lowest Common Multiple of 197,936 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 184392

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/184392

Therefore, the GCF of Fractions 975/197,689/936 is 13/184392

Least Common Multiple of 197,936 with GCF Formula

Least Common Multiple of 197,936 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 197,936 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(197,936) = 1

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

GCF(197,936) x common factors =1 x 1 = 1

LCM(197,936) = ( 197 × 936 ) / 1

LCM(197,936) = 184392 / 1

LCM(197,936) = 184392


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 975/197, 689/936

1. What is the HCF of 975,689?

The HCF of 975,689 is 13

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 975/197, 689/936?

Answer: GCF of Numerators as per given numbers 975/197, 689/936 is

GCF of Numerators i.e. for 975,689 is 13

LCM of denominators i.e. for 197,936 is 184392.

Thus, GCF of Fractions is 13/184392.Finally, GCF of Fractions for 975/197, 689/936 is 13/184392.