How to Find GCF of 2609/140, 6974/7958?

GCF of 2609/140, 6974/7958

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 2609/140, 6974/7958 i.e 1/557060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2609/140, 6974/7958.

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 2609/140,6974/7958?

Given fractions are 2609/140,6974/7958

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 2609/140,6974/7958, numerators are 2609,6974

Denominators are 140,7958

The GCF of 2609,6974 is 1 .

LCM of 140,7958 is 557060.

The greatest common factor of 2609/140,6974/7958 = [GCF of 2609,6974]/[LCM of 140,7958]= 1/557060

Therefore, the GCF of 2609/140,6974/7958 is 1/557060.

Greatest Common Factor of 2609,6974

To find the highest common factor of 2609,6974, we have to find the factors of both numbers and list the highest common factor.

The factors of 2609 are 1, 2609

The factors of 6974 are 1, 2, 11, 22, 317, 634, 3487, 6974

The HCF of 2609,6974 is 1.

Lets's calculate GCF of 2609,6974

Greatest Common Factor (GCF) of 2609,6974 By Common Division

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

Greatest Common Factor of 2609,6974 By Matching Biggest Common Factor Method

Now, list down the factors of 2609

1,2609

Now, list down the factors of 6974

1,2,11,22,317,634,3487,6974

Greatest Common Factor

We found the factors 2609,6974 . The biggest common factor number is the GCF number.
So the greatest common factor 2609,6974 is 1.

Lets's calculate LCM of 140,7958

Lowest Common Multiple of 140,7958 using Common Division

2	140, 7958
	70, 3979

∴ So the LCM of the given numbers is 2 x 70 x 3979 = 557060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/557060

Therefore, the GCF of Fractions 2609/140,6974/7958 is 1/557060

Least Common Multiple of 140,7958 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 140,7958 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(140,7958) = 2

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

GCF(140,7958) x common factors =2 x 1 = 2

LCM(140,7958) = ( 140 × 7958 ) / 2

LCM(140,7958) = 1114120 / 2

LCM(140,7958) = 557060

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FAQs on GCF of Fractions of 2609/140, 6974/7958

1. What is the HCF of 2609,6974?

The HCF of 2609,6974 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 2609/140, 6974/7958?

Answer: GCF of Numerators as per given numbers 2609/140, 6974/7958 is

GCF of Numerators i.e. for 2609,6974 is 1

LCM of denominators i.e. for 140,7958 is 557060.

Thus, GCF of Fractions is 1/557060.Finally, GCF of Fractions for 2609/140, 6974/7958 is 1/557060.