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GCF of 302/41, 686/254

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 302/41, 686/254 i.e 2/10414 easily. The following is the detailed procedure to determine the greatest common factor of fractions 302/41, 686/254.

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 302/41,686/254?

Given fractions are 302/41,686/254

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 302/41,686/254, numerators are 302,686

Denominators are 41,254

The GCF of 302,686 is 2 .

LCM of 41,254 is 10414.

The greatest common factor of 302/41,686/254 = [GCF of 302,686]/[LCM of 41,254]= 2/10414

Therefore, the GCF of 302/41,686/254 is 2/10414.

Greatest Common Factor of 302,686

To find the highest common factor of 302,686, we have to find the factors of both numbers and list the highest common factor.

The factors of 302 are 1, 2, 151, 302

The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686

The HCF of 302,686 is 2.

Lets's calculate GCF of 302,686

Greatest Common Factor (GCF) of 302,686 By Common Division

2 302, 686
151, 343

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

Greatest Common Factor of 302,686 By Matching Biggest Common Factor Method

Greatest Common Factor of 302,686 By Matching Biggest Common Factor Method

Now, list down the factors of 302

:

1,2,151,302

Now, list down the factors of 686

:

1,2,7,14,49,98,343,686

Greatest Common Factor

We found the factors 302,686 . The biggest common factor number is the GCF number.
So the greatest common factor 302,686 is 2.

Lets's calculate LCM of 41,254

Lowest Common Multiple of 41,254 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 10414

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10414

Therefore, the GCF of Fractions 302/41,686/254 is 2/10414

Least Common Multiple of 41,254 with GCF Formula

Least Common Multiple of 41,254 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 41,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(41,254) = 1

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

GCF(41,254) x common factors =1 x 1 = 1

LCM(41,254) = ( 41 × 254 ) / 1

LCM(41,254) = 10414 / 1

LCM(41,254) = 10414


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FAQs on GCF of Fractions of 302/41, 686/254

1. What is the HCF of 302,686?

The HCF of 302,686 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 302/41, 686/254?

Answer: GCF of Numerators as per given numbers 302/41, 686/254 is

GCF of Numerators i.e. for 302,686 is 2

LCM of denominators i.e. for 41,254 is 10414.

Thus, GCF of Fractions is 2/10414.Finally, GCF of Fractions for 302/41, 686/254 is 2/10414.