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GCF of 159/30, 351/109

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 159/30, 351/109 i.e 3/3270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 159/30, 351/109.

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 159/30,351/109?

Given fractions are 159/30,351/109

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 159/30,351/109, numerators are 159,351

Denominators are 30,109

The GCF of 159,351 is 3 .

LCM of 30,109 is 3270.

The greatest common factor of 159/30,351/109 = [GCF of 159,351]/[LCM of 30,109]= 3/3270

Therefore, the GCF of 159/30,351/109 is 3/3270.

Greatest Common Factor of 159,351

To find the highest common factor of 159,351, we have to find the factors of both numbers and list the highest common factor.

The factors of 159 are 1, 3, 53, 159

The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351

The HCF of 159,351 is 3.

Lets's calculate GCF of 159,351

Greatest Common Factor (GCF) of 159,351 By Common Division

3 159, 351
53, 117

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 159,351 By Matching Biggest Common Factor Method

Greatest Common Factor of 159,351 By Matching Biggest Common Factor Method

Now, list down the factors of 159

:

1,3,53,159

Now, list down the factors of 351

:

1,3,9,13,27,39,117,351

Greatest Common Factor

We found the factors 159,351 . The biggest common factor number is the GCF number.
So the greatest common factor 159,351 is 3.

Lets's calculate LCM of 30,109

Lowest Common Multiple of 30,109 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3270

Therefore, the GCF of Fractions 159/30,351/109 is 3/3270

Least Common Multiple of 30,109 with GCF Formula

Least Common Multiple of 30,109 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 30,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,109) = 1

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

GCF(30,109) x common factors =1 x 1 = 1

LCM(30,109) = ( 30 × 109 ) / 1

LCM(30,109) = 3270 / 1

LCM(30,109) = 3270


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FAQs on GCF of Fractions of 159/30, 351/109

1. What is the HCF of 159,351?

The HCF of 159,351 is 3

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 159/30, 351/109?

Answer: GCF of Numerators as per given numbers 159/30, 351/109 is

GCF of Numerators i.e. for 159,351 is 3

LCM of denominators i.e. for 30,109 is 3270.

Thus, GCF of Fractions is 3/3270.Finally, GCF of Fractions for 159/30, 351/109 is 3/3270.