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GCF of 293/214, 402/678

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 293/214, 402/678 i.e 1/72546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 293/214, 402/678.

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 293/214,402/678?

Given fractions are 293/214,402/678

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 293/214,402/678, numerators are 293,402

Denominators are 214,678

The GCF of 293,402 is 1 .

LCM of 214,678 is 72546.

The greatest common factor of 293/214,402/678 = [GCF of 293,402]/[LCM of 214,678]= 1/72546

Therefore, the GCF of 293/214,402/678 is 1/72546.

Greatest Common Factor of 293,402

To find the highest common factor of 293,402, we have to find the factors of both numbers and list the highest common factor.

The factors of 293 are 1, 293

The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402

The HCF of 293,402 is 1.

Lets's calculate GCF of 293,402

Greatest Common Factor (GCF) of 293,402 By Common Division

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

Greatest Common Factor of 293,402 By Matching Biggest Common Factor Method

Greatest Common Factor of 293,402 By Matching Biggest Common Factor Method

Now, list down the factors of 293

:

1,293

Now, list down the factors of 402

:

1,2,3,6,67,134,201,402

Greatest Common Factor

We found the factors 293,402 . The biggest common factor number is the GCF number.
So the greatest common factor 293,402 is 1.

Lets's calculate LCM of 214,678

Lowest Common Multiple of 214,678 using Common Division

2 214, 678
107, 339

∴ So the LCM of the given numbers is 2 x 107 x 339 = 72546

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72546

Therefore, the GCF of Fractions 293/214,402/678 is 1/72546

Least Common Multiple of 214,678 with GCF Formula

Least Common Multiple of 214,678 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 214,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,678) = 2

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

GCF(214,678) x common factors =2 x 1 = 2

LCM(214,678) = ( 214 × 678 ) / 2

LCM(214,678) = 145092 / 2

LCM(214,678) = 72546


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FAQs on GCF of Fractions of 293/214, 402/678

1. What is the HCF of 293,402?

The HCF of 293,402 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 293/214, 402/678?

Answer: GCF of Numerators as per given numbers 293/214, 402/678 is

GCF of Numerators i.e. for 293,402 is 1

LCM of denominators i.e. for 214,678 is 72546.

Thus, GCF of Fractions is 1/72546.Finally, GCF of Fractions for 293/214, 402/678 is 1/72546.