How to Find GCF of 9709/842, 8014/977?

GCF of 9709/842, 8014/977

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 9709/842, 8014/977 i.e 1/822634 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9709/842, 8014/977.

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 9709/842,8014/977?

Given fractions are 9709/842,8014/977

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 9709/842,8014/977, numerators are 9709,8014

Denominators are 842,977

The GCF of 9709,8014 is 1 .

LCM of 842,977 is 822634.

The greatest common factor of 9709/842,8014/977 = [GCF of 9709,8014]/[LCM of 842,977]= 1/822634

Therefore, the GCF of 9709/842,8014/977 is 1/822634.

Greatest Common Factor of 9709,8014

To find the highest common factor of 9709,8014, we have to find the factors of both numbers and list the highest common factor.

The factors of 9709 are 1, 7, 19, 73, 133, 511, 1387, 9709

The factors of 8014 are 1, 2, 4007, 8014

The HCF of 9709,8014 is 1.

Lets's calculate GCF of 9709,8014

Greatest Common Factor (GCF) of 9709,8014 By Common Division

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

Greatest Common Factor of 9709,8014 By Matching Biggest Common Factor Method

Now, list down the factors of 9709

1,7,19,73,133,511,1387,9709

Now, list down the factors of 8014

1,2,4007,8014

Greatest Common Factor

We found the factors 9709,8014 . The biggest common factor number is the GCF number.
So the greatest common factor 9709,8014 is 1.

Lets's calculate LCM of 842,977

Lowest Common Multiple of 842,977 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 822634

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/822634

Therefore, the GCF of Fractions 9709/842,8014/977 is 1/822634

Least Common Multiple of 842,977 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 842,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(842,977) = 1

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

GCF(842,977) x common factors =1 x 1 = 1

LCM(842,977) = ( 842 × 977 ) / 1

LCM(842,977) = 822634 / 1

LCM(842,977) = 822634

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FAQs on GCF of Fractions of 9709/842, 8014/977

1. What is the HCF of 9709,8014?

The HCF of 9709,8014 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 9709/842, 8014/977?

Answer: GCF of Numerators as per given numbers 9709/842, 8014/977 is

GCF of Numerators i.e. for 9709,8014 is 1

LCM of denominators i.e. for 842,977 is 822634.

Thus, GCF of Fractions is 1/822634.Finally, GCF of Fractions for 9709/842, 8014/977 is 1/822634.