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GCF of 102/290, 278/179

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 102/290, 278/179 i.e 2/51910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/290, 278/179.

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 102/290,278/179?

Given fractions are 102/290,278/179

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 102/290,278/179, numerators are 102,278

Denominators are 290,179

The GCF of 102,278 is 2 .

LCM of 290,179 is 51910.

The greatest common factor of 102/290,278/179 = [GCF of 102,278]/[LCM of 290,179]= 2/51910

Therefore, the GCF of 102/290,278/179 is 2/51910.

Greatest Common Factor of 102,278

To find the highest common factor of 102,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102

The factors of 278 are 1, 2, 139, 278

The HCF of 102,278 is 2.

Lets's calculate GCF of 102,278

Greatest Common Factor (GCF) of 102,278 By Common Division

2 102, 278
51, 139

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 102,278 By Matching Biggest Common Factor Method

Greatest Common Factor of 102,278 By Matching Biggest Common Factor Method

Now, list down the factors of 102

:

1,2,3,6,17,34,51,102

Now, list down the factors of 278

:

1,2,139,278

Greatest Common Factor

We found the factors 102,278 . The biggest common factor number is the GCF number.
So the greatest common factor 102,278 is 2.

Lets's calculate LCM of 290,179

Lowest Common Multiple of 290,179 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 51910

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/51910

Therefore, the GCF of Fractions 102/290,278/179 is 2/51910

Least Common Multiple of 290,179 with GCF Formula

Least Common Multiple of 290,179 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 290,179 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(290,179) = 1

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

GCF(290,179) x common factors =1 x 1 = 1

LCM(290,179) = ( 290 × 179 ) / 1

LCM(290,179) = 51910 / 1

LCM(290,179) = 51910


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FAQs on GCF of Fractions of 102/290, 278/179

1. What is the HCF of 102,278?

The HCF of 102,278 is 2

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 102/290, 278/179?

Answer: GCF of Numerators as per given numbers 102/290, 278/179 is

GCF of Numerators i.e. for 102,278 is 2

LCM of denominators i.e. for 290,179 is 51910.

Thus, GCF of Fractions is 2/51910.Finally, GCF of Fractions for 102/290, 278/179 is 2/51910.