How to Find GCF of 9697/228, 1314/2083?

GCF of 9697/228, 1314/2083

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 9697/228, 1314/2083 i.e 1/474924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9697/228, 1314/2083.

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 9697/228,1314/2083?

Given fractions are 9697/228,1314/2083

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 9697/228,1314/2083, numerators are 9697,1314

Denominators are 228,2083

The GCF of 9697,1314 is 1 .

LCM of 228,2083 is 474924.

The greatest common factor of 9697/228,1314/2083 = [GCF of 9697,1314]/[LCM of 228,2083]= 1/474924

Therefore, the GCF of 9697/228,1314/2083 is 1/474924.

Greatest Common Factor of 9697,1314

To find the highest common factor of 9697,1314, we have to find the factors of both numbers and list the highest common factor.

The factors of 9697 are 1, 9697

The factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314

The HCF of 9697,1314 is 1.

Lets's calculate GCF of 9697,1314

Greatest Common Factor (GCF) of 9697,1314 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 9697,1314 By Matching Biggest Common Factor Method

Now, list down the factors of 9697

1,9697

Now, list down the factors of 1314

1,2,3,6,9,18,73,146,219,438,657,1314

Greatest Common Factor

We found the factors 9697,1314 . The biggest common factor number is the GCF number.
So the greatest common factor 9697,1314 is 1.

Lets's calculate LCM of 228,2083

Lowest Common Multiple of 228,2083 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 474924

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/474924

Therefore, the GCF of Fractions 9697/228,1314/2083 is 1/474924

Least Common Multiple of 228,2083 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 228,2083 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(228,2083) = 1

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

GCF(228,2083) x common factors =1 x 1 = 1

LCM(228,2083) = ( 228 × 2083 ) / 1

LCM(228,2083) = 474924 / 1

LCM(228,2083) = 474924

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FAQs on GCF of Fractions of 9697/228, 1314/2083

1. What is the HCF of 9697,1314?

The HCF of 9697,1314 is 1

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 9697/228, 1314/2083?

Answer: GCF of Numerators as per given numbers 9697/228, 1314/2083 is

GCF of Numerators i.e. for 9697,1314 is 1

LCM of denominators i.e. for 228,2083 is 474924.

Thus, GCF of Fractions is 1/474924.Finally, GCF of Fractions for 9697/228, 1314/2083 is 1/474924.