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GCF of 340/374, 697/679

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 340/374, 697/679 i.e 17/253946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/374, 697/679.

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 340/374,697/679?

Given fractions are 340/374,697/679

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 340/374,697/679, numerators are 340,697

Denominators are 374,679

The GCF of 340,697 is 17 .

LCM of 374,679 is 253946.

The greatest common factor of 340/374,697/679 = [GCF of 340,697]/[LCM of 374,679]= 17/253946

Therefore, the GCF of 340/374,697/679 is 17/253946.

Greatest Common Factor of 340,697

To find the highest common factor of 340,697, we have to find the factors of both numbers and list the highest common factor.

The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

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

The HCF of 340,697 is 17.

Lets's calculate GCF of 340,697

Greatest Common Factor (GCF) of 340,697 By Common Division

17 340, 697
20, 41

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

Greatest Common Factor of 340,697 By Matching Biggest Common Factor Method

Greatest Common Factor of 340,697 By Matching Biggest Common Factor Method

Now, list down the factors of 340

:

1,2,4,5,10,17,20,34,68,85,170,340

Now, list down the factors of 697

:

1,17,41,697

Greatest Common Factor

We found the factors 340,697 . The biggest common factor number is the GCF number.
So the greatest common factor 340,697 is 17.

Lets's calculate LCM of 374,679

Lowest Common Multiple of 374,679 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 253946

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/253946

Therefore, the GCF of Fractions 340/374,697/679 is 17/253946

Least Common Multiple of 374,679 with GCF Formula

Least Common Multiple of 374,679 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 374,679 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(374,679) = 1

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

GCF(374,679) x common factors =1 x 1 = 1

LCM(374,679) = ( 374 × 679 ) / 1

LCM(374,679) = 253946 / 1

LCM(374,679) = 253946


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FAQs on GCF of Fractions of 340/374, 697/679

1. What is the HCF of 340,697?

The HCF of 340,697 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 340/374, 697/679?

Answer: GCF of Numerators as per given numbers 340/374, 697/679 is

GCF of Numerators i.e. for 340,697 is 17

LCM of denominators i.e. for 374,679 is 253946.

Thus, GCF of Fractions is 17/253946.Finally, GCF of Fractions for 340/374, 697/679 is 17/253946.