How to Find GCF of 714/691, 954/619?

GCF of 714/691, 954/619

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 714/691, 954/619 i.e 6/427729 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/691, 954/619.

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 714/691,954/619?

Given fractions are 714/691,954/619

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 714/691,954/619, numerators are 714,954

Denominators are 691,619

The GCF of 714,954 is 6 .

LCM of 691,619 is 427729.

The greatest common factor of 714/691,954/619 = [GCF of 714,954]/[LCM of 691,619]= 6/427729

Therefore, the GCF of 714/691,954/619 is 6/427729.

Greatest Common Factor of 714,954

To find the highest common factor of 714,954, we have to find the factors of both numbers and list the highest common factor.

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

The factors of 954 are 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954

The HCF of 714,954 is 6.

Lets's calculate GCF of 714,954

Greatest Common Factor (GCF) of 714,954 By Common Division

2	714, 954
3	357, 477
	119, 159

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 714,954 By Matching Biggest Common Factor Method

Now, list down the factors of 714

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Now, list down the factors of 954

1,2,3,6,9,18,53,106,159,318,477,954

Greatest Common Factor

We found the factors 714,954 . The biggest common factor number is the GCF number.
So the greatest common factor 714,954 is 6.

Lets's calculate LCM of 691,619

Lowest Common Multiple of 691,619 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 427729

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/427729

Therefore, the GCF of Fractions 714/691,954/619 is 6/427729

Least Common Multiple of 691,619 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 691,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(691,619) = 1

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

GCF(691,619) x common factors =1 x 1 = 1

LCM(691,619) = ( 691 × 619 ) / 1

LCM(691,619) = 427729 / 1

LCM(691,619) = 427729

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FAQs on GCF of Fractions of 714/691, 954/619

1. What is the HCF of 714,954?

The HCF of 714,954 is 6

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 714/691, 954/619?

Answer: GCF of Numerators as per given numbers 714/691, 954/619 is

GCF of Numerators i.e. for 714,954 is 6

LCM of denominators i.e. for 691,619 is 427729.

Thus, GCF of Fractions is 6/427729.Finally, GCF of Fractions for 714/691, 954/619 is 6/427729.