How to Find GCF of 997/266, 2109/6000?

GCF of 997/266, 2109/6000

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 997/266, 2109/6000 i.e 1/798000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 997/266, 2109/6000.

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 997/266,2109/6000?

Given fractions are 997/266,2109/6000

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 997/266,2109/6000, numerators are 997,2109

Denominators are 266,6000

The GCF of 997,2109 is 1 .

LCM of 266,6000 is 798000.

The greatest common factor of 997/266,2109/6000 = [GCF of 997,2109]/[LCM of 266,6000]= 1/798000

Therefore, the GCF of 997/266,2109/6000 is 1/798000.

Greatest Common Factor of 997,2109

To find the highest common factor of 997,2109, we have to find the factors of both numbers and list the highest common factor.

The factors of 997 are 1, 997

The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109

The HCF of 997,2109 is 1.

Lets's calculate GCF of 997,2109

Greatest Common Factor (GCF) of 997,2109 By Common Division

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

Greatest Common Factor of 997,2109 By Matching Biggest Common Factor Method

Now, list down the factors of 997

1,997

Now, list down the factors of 2109

1,3,19,37,57,111,703,2109

Greatest Common Factor

We found the factors 997,2109 . The biggest common factor number is the GCF number.
So the greatest common factor 997,2109 is 1.

Lets's calculate LCM of 266,6000

Lowest Common Multiple of 266,6000 using Common Division

2	266, 6000
	133, 3000

∴ So the LCM of the given numbers is 2 x 133 x 3000 = 798000

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/798000

Therefore, the GCF of Fractions 997/266,2109/6000 is 1/798000

Least Common Multiple of 266,6000 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 266,6000 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(266,6000) = 2

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

GCF(266,6000) x common factors =2 x 1 = 2

LCM(266,6000) = ( 266 × 6000 ) / 2

LCM(266,6000) = 1596000 / 2

LCM(266,6000) = 798000

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FAQs on GCF of Fractions of 997/266, 2109/6000

1. What is the HCF of 997,2109?

The HCF of 997,2109 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 997/266, 2109/6000?

Answer: GCF of Numerators as per given numbers 997/266, 2109/6000 is

GCF of Numerators i.e. for 997,2109 is 1

LCM of denominators i.e. for 266,6000 is 798000.

Thus, GCF of Fractions is 1/798000.Finally, GCF of Fractions for 997/266, 2109/6000 is 1/798000.