How to Find GCF of 714/857, 505/414?

GCF of 714/857, 505/414

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 714/857, 505/414 i.e 1/354798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/857, 505/414.

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 714/857,505/414?

Given fractions are 714/857,505/414

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 714/857,505/414, numerators are 714,505

Denominators are 857,414

The GCF of 714,505 is 1 .

LCM of 857,414 is 354798.

The greatest common factor of 714/857,505/414 = [GCF of 714,505]/[LCM of 857,414]= 1/354798

Therefore, the GCF of 714/857,505/414 is 1/354798.

Greatest Common Factor of 714,505

To find the highest common factor of 714,505, 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 505 are 1, 5, 101, 505

The HCF of 714,505 is 1.

Lets's calculate GCF of 714,505

Greatest Common Factor (GCF) of 714,505 By Common Division

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

Greatest Common Factor of 714,505 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 505

1,5,101,505

Greatest Common Factor

We found the factors 714,505 . The biggest common factor number is the GCF number.
So the greatest common factor 714,505 is 1.

Lets's calculate LCM of 857,414

Lowest Common Multiple of 857,414 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 354798

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/354798

Therefore, the GCF of Fractions 714/857,505/414 is 1/354798

Least Common Multiple of 857,414 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 857,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(857,414) = 1

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

GCF(857,414) x common factors =1 x 1 = 1

LCM(857,414) = ( 857 × 414 ) / 1

LCM(857,414) = 354798 / 1

LCM(857,414) = 354798

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FAQs on GCF of Fractions of 714/857, 505/414

1. What is the HCF of 714,505?

The HCF of 714,505 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 714/857, 505/414?

Answer: GCF of Numerators as per given numbers 714/857, 505/414 is

GCF of Numerators i.e. for 714,505 is 1

LCM of denominators i.e. for 857,414 is 354798.

Thus, GCF of Fractions is 1/354798.Finally, GCF of Fractions for 714/857, 505/414 is 1/354798.