How to Find GCF of 9707/823, 9674/1022?

GCF of 9707/823, 9674/1022

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 9707/823, 9674/1022 i.e 1/841106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9707/823, 9674/1022.

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 9707/823,9674/1022?

Given fractions are 9707/823,9674/1022

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 9707/823,9674/1022, numerators are 9707,9674

Denominators are 823,1022

The GCF of 9707,9674 is 1 .

LCM of 823,1022 is 841106.

The greatest common factor of 9707/823,9674/1022 = [GCF of 9707,9674]/[LCM of 823,1022]= 1/841106

Therefore, the GCF of 9707/823,9674/1022 is 1/841106.

Greatest Common Factor of 9707,9674

To find the highest common factor of 9707,9674, we have to find the factors of both numbers and list the highest common factor.

The factors of 9707 are 1, 17, 571, 9707

The factors of 9674 are 1, 2, 7, 14, 691, 1382, 4837, 9674

The HCF of 9707,9674 is 1.

Lets's calculate GCF of 9707,9674

Greatest Common Factor (GCF) of 9707,9674 By Common Division

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

Greatest Common Factor of 9707,9674 By Matching Biggest Common Factor Method

Now, list down the factors of 9707

1,17,571,9707

Now, list down the factors of 9674

1,2,7,14,691,1382,4837,9674

Greatest Common Factor

We found the factors 9707,9674 . The biggest common factor number is the GCF number.
So the greatest common factor 9707,9674 is 1.

Lets's calculate LCM of 823,1022

Lowest Common Multiple of 823,1022 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 841106

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/841106

Therefore, the GCF of Fractions 9707/823,9674/1022 is 1/841106

Least Common Multiple of 823,1022 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 823,1022 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(823,1022) = 1

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

GCF(823,1022) x common factors =1 x 1 = 1

LCM(823,1022) = ( 823 × 1022 ) / 1

LCM(823,1022) = 841106 / 1

LCM(823,1022) = 841106

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FAQs on GCF of Fractions of 9707/823, 9674/1022

1. What is the HCF of 9707,9674?

The HCF of 9707,9674 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 9707/823, 9674/1022?

Answer: GCF of Numerators as per given numbers 9707/823, 9674/1022 is

GCF of Numerators i.e. for 9707,9674 is 1

LCM of denominators i.e. for 823,1022 is 841106.

Thus, GCF of Fractions is 1/841106.Finally, GCF of Fractions for 9707/823, 9674/1022 is 1/841106.