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GCF of 294/76, 434/686

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 294/76, 434/686 i.e 14/26068 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/76, 434/686.

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 294/76,434/686?

Given fractions are 294/76,434/686

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 294/76,434/686, numerators are 294,434

Denominators are 76,686

The GCF of 294,434 is 14 .

LCM of 76,686 is 26068.

The greatest common factor of 294/76,434/686 = [GCF of 294,434]/[LCM of 76,686]= 14/26068

Therefore, the GCF of 294/76,434/686 is 14/26068.

Greatest Common Factor of 294,434

To find the highest common factor of 294,434, we have to find the factors of both numbers and list the highest common factor.

The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434

The HCF of 294,434 is 14.

Lets's calculate GCF of 294,434

Greatest Common Factor (GCF) of 294,434 By Common Division

2 294, 434
7 147, 217
21, 31

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 294,434 By Matching Biggest Common Factor Method

Greatest Common Factor of 294,434 By Matching Biggest Common Factor Method

Now, list down the factors of 294

:

1,2,3,6,7,14,21,42,49,98,147,294

Now, list down the factors of 434

:

1,2,7,14,31,62,217,434

Greatest Common Factor

We found the factors 294,434 . The biggest common factor number is the GCF number.
So the greatest common factor 294,434 is 14.

Lets's calculate LCM of 76,686

Lowest Common Multiple of 76,686 using Common Division

2 76, 686
38, 343

∴ So the LCM of the given numbers is 2 x 38 x 343 = 26068

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/26068

Therefore, the GCF of Fractions 294/76,434/686 is 14/26068

Least Common Multiple of 76,686 with GCF Formula

Least Common Multiple of 76,686 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 76,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,686) = 2

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

GCF(76,686) x common factors =2 x 1 = 2

LCM(76,686) = ( 76 × 686 ) / 2

LCM(76,686) = 52136 / 2

LCM(76,686) = 26068


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FAQs on GCF of Fractions of 294/76, 434/686

1. What is the HCF of 294,434?

The HCF of 294,434 is 14

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 294/76, 434/686?

Answer: GCF of Numerators as per given numbers 294/76, 434/686 is

GCF of Numerators i.e. for 294,434 is 14

LCM of denominators i.e. for 76,686 is 26068.

Thus, GCF of Fractions is 14/26068.Finally, GCF of Fractions for 294/76, 434/686 is 14/26068.