How to Find GCF of 340/314, 5910/691?

GCF of 340/314, 5910/691

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 340/314, 5910/691 i.e 10/216974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/314, 5910/691.

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 340/314,5910/691?

Given fractions are 340/314,5910/691

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 340/314,5910/691, numerators are 340,5910

Denominators are 314,691

The GCF of 340,5910 is 10 .

LCM of 314,691 is 216974.

The greatest common factor of 340/314,5910/691 = [GCF of 340,5910]/[LCM of 314,691]= 10/216974

Therefore, the GCF of 340/314,5910/691 is 10/216974.

Greatest Common Factor of 340,5910

To find the highest common factor of 340,5910, 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 5910 are 1, 2, 3, 5, 6, 10, 15, 30, 197, 394, 591, 985, 1182, 1970, 2955, 5910

The HCF of 340,5910 is 10.

Lets's calculate GCF of 340,5910

Greatest Common Factor (GCF) of 340,5910 By Common Division

2	340, 5910
5	170, 2955
	34, 591

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 340,5910 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 5910

1,2,3,5,6,10,15,30,197,394,591,985,1182,1970,2955,5910

Greatest Common Factor

We found the factors 340,5910 . The biggest common factor number is the GCF number.
So the greatest common factor 340,5910 is 10.

Lets's calculate LCM of 314,691

Lowest Common Multiple of 314,691 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 216974

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/216974

Therefore, the GCF of Fractions 340/314,5910/691 is 10/216974

Least Common Multiple of 314,691 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 314,691 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,691) = 1

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

GCF(314,691) x common factors =1 x 1 = 1

LCM(314,691) = ( 314 × 691 ) / 1

LCM(314,691) = 216974 / 1

LCM(314,691) = 216974

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FAQs on GCF of Fractions of 340/314, 5910/691

1. What is the HCF of 340,5910?

The HCF of 340,5910 is 10

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 340/314, 5910/691?

Answer: GCF of Numerators as per given numbers 340/314, 5910/691 is

GCF of Numerators i.e. for 340,5910 is 10

LCM of denominators i.e. for 314,691 is 216974.

Thus, GCF of Fractions is 10/216974.Finally, GCF of Fractions for 340/314, 5910/691 is 10/216974.