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GCF of 986/41, 697/406

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 986/41, 697/406 i.e 17/16646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 986/41, 697/406.

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 986/41,697/406?

Given fractions are 986/41,697/406

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 986/41,697/406, numerators are 986,697

Denominators are 41,406

The GCF of 986,697 is 17 .

LCM of 41,406 is 16646.

The greatest common factor of 986/41,697/406 = [GCF of 986,697]/[LCM of 41,406]= 17/16646

Therefore, the GCF of 986/41,697/406 is 17/16646.

Greatest Common Factor of 986,697

To find the highest common factor of 986,697, we have to find the factors of both numbers and list the highest common factor.

The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986

The factors of 697 are 1, 17, 41, 697

The HCF of 986,697 is 17.

Lets's calculate GCF of 986,697

Greatest Common Factor (GCF) of 986,697 By Common Division

17 986, 697
58, 41

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 986,697 By Matching Biggest Common Factor Method

Greatest Common Factor of 986,697 By Matching Biggest Common Factor Method

Now, list down the factors of 986

:

1,2,17,29,34,58,493,986

Now, list down the factors of 697

:

1,17,41,697

Greatest Common Factor

We found the factors 986,697 . The biggest common factor number is the GCF number.
So the greatest common factor 986,697 is 17.

Lets's calculate LCM of 41,406

Lowest Common Multiple of 41,406 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 16646

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/16646

Therefore, the GCF of Fractions 986/41,697/406 is 17/16646

Least Common Multiple of 41,406 with GCF Formula

Least Common Multiple of 41,406 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 41,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(41,406) = 1

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

GCF(41,406) x common factors =1 x 1 = 1

LCM(41,406) = ( 41 × 406 ) / 1

LCM(41,406) = 16646 / 1

LCM(41,406) = 16646


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FAQs on GCF of Fractions of 986/41, 697/406

1. What is the HCF of 986,697?

The HCF of 986,697 is 17

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 986/41, 697/406?

Answer: GCF of Numerators as per given numbers 986/41, 697/406 is

GCF of Numerators i.e. for 986,697 is 17

LCM of denominators i.e. for 41,406 is 16646.

Thus, GCF of Fractions is 17/16646.Finally, GCF of Fractions for 986/41, 697/406 is 17/16646.