How to Find GCF of 514/506, 357/835?

GCF of 514/506, 357/835

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 514/506, 357/835 i.e 1/422510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/506, 357/835.

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 514/506,357/835?

Given fractions are 514/506,357/835

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 514/506,357/835, numerators are 514,357

Denominators are 506,835

The GCF of 514,357 is 1 .

LCM of 506,835 is 422510.

The greatest common factor of 514/506,357/835 = [GCF of 514,357]/[LCM of 506,835]= 1/422510

Therefore, the GCF of 514/506,357/835 is 1/422510.

Greatest Common Factor of 514,357

To find the highest common factor of 514,357, we have to find the factors of both numbers and list the highest common factor.

The factors of 514 are 1, 2, 257, 514

The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357

The HCF of 514,357 is 1.

Lets's calculate GCF of 514,357

Greatest Common Factor (GCF) of 514,357 By Common Division

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

Greatest Common Factor of 514,357 By Matching Biggest Common Factor Method

Now, list down the factors of 514

1,2,257,514

Now, list down the factors of 357

1,3,7,17,21,51,119,357

Greatest Common Factor

We found the factors 514,357 . The biggest common factor number is the GCF number.
So the greatest common factor 514,357 is 1.

Lets's calculate LCM of 506,835

Lowest Common Multiple of 506,835 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 422510

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/422510

Therefore, the GCF of Fractions 514/506,357/835 is 1/422510

Least Common Multiple of 506,835 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 506,835 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(506,835) = 1

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

GCF(506,835) x common factors =1 x 1 = 1

LCM(506,835) = ( 506 × 835 ) / 1

LCM(506,835) = 422510 / 1

LCM(506,835) = 422510

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FAQs on GCF of Fractions of 514/506, 357/835

1. What is the HCF of 514,357?

The HCF of 514,357 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 514/506, 357/835?

Answer: GCF of Numerators as per given numbers 514/506, 357/835 is

GCF of Numerators i.e. for 514,357 is 1

LCM of denominators i.e. for 506,835 is 422510.

Thus, GCF of Fractions is 1/422510.Finally, GCF of Fractions for 514/506, 357/835 is 1/422510.