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GCF of 187/302, 509/706

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 187/302, 509/706 i.e 1/106606 easily. The following is the detailed procedure to determine the greatest common factor of fractions 187/302, 509/706.

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 187/302,509/706?

Given fractions are 187/302,509/706

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 187/302,509/706, numerators are 187,509

Denominators are 302,706

The GCF of 187,509 is 1 .

LCM of 302,706 is 106606.

The greatest common factor of 187/302,509/706 = [GCF of 187,509]/[LCM of 302,706]= 1/106606

Therefore, the GCF of 187/302,509/706 is 1/106606.

Greatest Common Factor of 187,509

To find the highest common factor of 187,509, we have to find the factors of both numbers and list the highest common factor.

The factors of 187 are 1, 11, 17, 187

The factors of 509 are 1, 509

The HCF of 187,509 is 1.

Lets's calculate GCF of 187,509

Greatest Common Factor (GCF) of 187,509 By Common Division

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

Greatest Common Factor of 187,509 By Matching Biggest Common Factor Method

Greatest Common Factor of 187,509 By Matching Biggest Common Factor Method

Now, list down the factors of 187

:

1,11,17,187

Now, list down the factors of 509

:

1,509

Greatest Common Factor

We found the factors 187,509 . The biggest common factor number is the GCF number.
So the greatest common factor 187,509 is 1.

Lets's calculate LCM of 302,706

Lowest Common Multiple of 302,706 using Common Division

2 302, 706
151, 353

∴ So the LCM of the given numbers is 2 x 151 x 353 = 106606

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/106606

Therefore, the GCF of Fractions 187/302,509/706 is 1/106606

Least Common Multiple of 302,706 with GCF Formula

Least Common Multiple of 302,706 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 302,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(302,706) = 2

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

GCF(302,706) x common factors =2 x 1 = 2

LCM(302,706) = ( 302 × 706 ) / 2

LCM(302,706) = 213212 / 2

LCM(302,706) = 106606


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FAQs on GCF of Fractions of 187/302, 509/706

1. What is the HCF of 187,509?

The HCF of 187,509 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 187/302, 509/706?

Answer: GCF of Numerators as per given numbers 187/302, 509/706 is

GCF of Numerators i.e. for 187,509 is 1

LCM of denominators i.e. for 302,706 is 106606.

Thus, GCF of Fractions is 1/106606.Finally, GCF of Fractions for 187/302, 509/706 is 1/106606.