How to Find GCF of 3497/971, 7683/6702?

GCF of 3497/971, 7683/6702

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 3497/971, 7683/6702 i.e 13/6507642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3497/971, 7683/6702.

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 3497/971,7683/6702?

Given fractions are 3497/971,7683/6702

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 3497/971,7683/6702, numerators are 3497,7683

Denominators are 971,6702

The GCF of 3497,7683 is 13 .

LCM of 971,6702 is 6507642.

The greatest common factor of 3497/971,7683/6702 = [GCF of 3497,7683]/[LCM of 971,6702]= 13/6507642

Therefore, the GCF of 3497/971,7683/6702 is 13/6507642.

Greatest Common Factor of 3497,7683

To find the highest common factor of 3497,7683, we have to find the factors of both numbers and list the highest common factor.

The factors of 3497 are 1, 13, 269, 3497

The factors of 7683 are 1, 3, 13, 39, 197, 591, 2561, 7683

The HCF of 3497,7683 is 13.

Lets's calculate GCF of 3497,7683

Greatest Common Factor (GCF) of 3497,7683 By Common Division

13	3497, 7683
	269, 591

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

Greatest Common Factor of 3497,7683 By Matching Biggest Common Factor Method

Now, list down the factors of 3497

1,13,269,3497

Now, list down the factors of 7683

1,3,13,39,197,591,2561,7683

Greatest Common Factor

We found the factors 3497,7683 . The biggest common factor number is the GCF number.
So the greatest common factor 3497,7683 is 13.

Lets's calculate LCM of 971,6702

Lowest Common Multiple of 971,6702 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 6507642

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/6507642

Therefore, the GCF of Fractions 3497/971,7683/6702 is 13/6507642

Least Common Multiple of 971,6702 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 971,6702 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(971,6702) = 1

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

GCF(971,6702) x common factors =1 x 1 = 1

LCM(971,6702) = ( 971 × 6702 ) / 1

LCM(971,6702) = 6507642 / 1

LCM(971,6702) = 6507642

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 3497/971, 7683/6702

1. What is the HCF of 3497,7683?

The HCF of 3497,7683 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 3497/971, 7683/6702?

Answer: GCF of Numerators as per given numbers 3497/971, 7683/6702 is

GCF of Numerators i.e. for 3497,7683 is 13

LCM of denominators i.e. for 971,6702 is 6507642.

Thus, GCF of Fractions is 13/6507642.Finally, GCF of Fractions for 3497/971, 7683/6702 is 13/6507642.