How to Find GCF of 997/978, 2074/6915?

GCF of 997/978, 2074/6915

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 997/978, 2074/6915 i.e 1/2254290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 997/978, 2074/6915.

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 997/978,2074/6915?

Given fractions are 997/978,2074/6915

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 997/978,2074/6915, numerators are 997,2074

Denominators are 978,6915

The GCF of 997,2074 is 1 .

LCM of 978,6915 is 2254290.

The greatest common factor of 997/978,2074/6915 = [GCF of 997,2074]/[LCM of 978,6915]= 1/2254290

Therefore, the GCF of 997/978,2074/6915 is 1/2254290.

Greatest Common Factor of 997,2074

To find the highest common factor of 997,2074, 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 2074 are 1, 2, 17, 34, 61, 122, 1037, 2074

The HCF of 997,2074 is 1.

Lets's calculate GCF of 997,2074

Greatest Common Factor (GCF) of 997,2074 By Common Division

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

Greatest Common Factor of 997,2074 By Matching Biggest Common Factor Method

Now, list down the factors of 997

1,997

Now, list down the factors of 2074

1,2,17,34,61,122,1037,2074

Greatest Common Factor

We found the factors 997,2074 . The biggest common factor number is the GCF number.
So the greatest common factor 997,2074 is 1.

Lets's calculate LCM of 978,6915

Lowest Common Multiple of 978,6915 using Common Division

3	978, 6915
	326, 2305

∴ So the LCM of the given numbers is 3 x 326 x 2305 = 2254290

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2254290

Therefore, the GCF of Fractions 997/978,2074/6915 is 1/2254290

Least Common Multiple of 978,6915 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 978,6915 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,6915) = 3

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

GCF(978,6915) x common factors =3 x 1 = 3

LCM(978,6915) = ( 978 × 6915 ) / 3

LCM(978,6915) = 6762870 / 3

LCM(978,6915) = 2254290

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FAQs on GCF of Fractions of 997/978, 2074/6915

1. What is the HCF of 997,2074?

The HCF of 997,2074 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 997/978, 2074/6915?

Answer: GCF of Numerators as per given numbers 997/978, 2074/6915 is

GCF of Numerators i.e. for 997,2074 is 1

LCM of denominators i.e. for 978,6915 is 2254290.

Thus, GCF of Fractions is 1/2254290.Finally, GCF of Fractions for 997/978, 2074/6915 is 1/2254290.