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GCF of 682/37, 209/978

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 682/37, 209/978 i.e 11/36186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/37, 209/978.

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 682/37,209/978?

Given fractions are 682/37,209/978

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 682/37,209/978, numerators are 682,209

Denominators are 37,978

The GCF of 682,209 is 11 .

LCM of 37,978 is 36186.

The greatest common factor of 682/37,209/978 = [GCF of 682,209]/[LCM of 37,978]= 11/36186

Therefore, the GCF of 682/37,209/978 is 11/36186.

Greatest Common Factor of 682,209

To find the highest common factor of 682,209, we have to find the factors of both numbers and list the highest common factor.

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The factors of 209 are 1, 11, 19, 209

The HCF of 682,209 is 11.

Lets's calculate GCF of 682,209

Greatest Common Factor (GCF) of 682,209 By Common Division

11 682, 209
62, 19

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 682,209 By Matching Biggest Common Factor Method

Greatest Common Factor of 682,209 By Matching Biggest Common Factor Method

Now, list down the factors of 682

:

1,2,11,22,31,62,341,682

Now, list down the factors of 209

:

1,11,19,209

Greatest Common Factor

We found the factors 682,209 . The biggest common factor number is the GCF number.
So the greatest common factor 682,209 is 11.

Lets's calculate LCM of 37,978

Lowest Common Multiple of 37,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 36186

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/36186

Therefore, the GCF of Fractions 682/37,209/978 is 11/36186

Least Common Multiple of 37,978 with GCF Formula

Least Common Multiple of 37,978 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 37,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,978) = 1

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

GCF(37,978) x common factors =1 x 1 = 1

LCM(37,978) = ( 37 × 978 ) / 1

LCM(37,978) = 36186 / 1

LCM(37,978) = 36186


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FAQs on GCF of Fractions of 682/37, 209/978

1. What is the HCF of 682,209?

The HCF of 682,209 is 11

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 682/37, 209/978?

Answer: GCF of Numerators as per given numbers 682/37, 209/978 is

GCF of Numerators i.e. for 682,209 is 11

LCM of denominators i.e. for 37,978 is 36186.

Thus, GCF of Fractions is 11/36186.Finally, GCF of Fractions for 682/37, 209/978 is 11/36186.