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GCF of 406/208, 322/678

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 406/208, 322/678 i.e 14/70512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/208, 322/678.

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 406/208,322/678?

Given fractions are 406/208,322/678

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 406/208,322/678, numerators are 406,322

Denominators are 208,678

The GCF of 406,322 is 14 .

LCM of 208,678 is 70512.

The greatest common factor of 406/208,322/678 = [GCF of 406,322]/[LCM of 208,678]= 14/70512

Therefore, the GCF of 406/208,322/678 is 14/70512.

Greatest Common Factor of 406,322

To find the highest common factor of 406,322, we have to find the factors of both numbers and list the highest common factor.

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322

The HCF of 406,322 is 14.

Lets's calculate GCF of 406,322

Greatest Common Factor (GCF) of 406,322 By Common Division

2 406, 322
7 203, 161
29, 23

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

Greatest Common Factor of 406,322 By Matching Biggest Common Factor Method

Greatest Common Factor of 406,322 By Matching Biggest Common Factor Method

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Now, list down the factors of 322

:

1,2,7,14,23,46,161,322

Greatest Common Factor

We found the factors 406,322 . The biggest common factor number is the GCF number.
So the greatest common factor 406,322 is 14.

Lets's calculate LCM of 208,678

Lowest Common Multiple of 208,678 using Common Division

2 208, 678
104, 339

∴ So the LCM of the given numbers is 2 x 104 x 339 = 70512

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/70512

Therefore, the GCF of Fractions 406/208,322/678 is 14/70512

Least Common Multiple of 208,678 with GCF Formula

Least Common Multiple of 208,678 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 208,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,678) = 2

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

GCF(208,678) x common factors =2 x 1 = 2

LCM(208,678) = ( 208 × 678 ) / 2

LCM(208,678) = 141024 / 2

LCM(208,678) = 70512


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FAQs on GCF of Fractions of 406/208, 322/678

1. What is the HCF of 406,322?

The HCF of 406,322 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 406/208, 322/678?

Answer: GCF of Numerators as per given numbers 406/208, 322/678 is

GCF of Numerators i.e. for 406,322 is 14

LCM of denominators i.e. for 208,678 is 70512.

Thus, GCF of Fractions is 14/70512.Finally, GCF of Fractions for 406/208, 322/678 is 14/70512.