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GCF of 786/204, 406/268

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 786/204, 406/268 i.e 2/13668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 786/204, 406/268.

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 786/204,406/268?

Given fractions are 786/204,406/268

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 786/204,406/268, numerators are 786,406

Denominators are 204,268

The GCF of 786,406 is 2 .

LCM of 204,268 is 13668.

The greatest common factor of 786/204,406/268 = [GCF of 786,406]/[LCM of 204,268]= 2/13668

Therefore, the GCF of 786/204,406/268 is 2/13668.

Greatest Common Factor of 786,406

To find the highest common factor of 786,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786

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

The HCF of 786,406 is 2.

Lets's calculate GCF of 786,406

Greatest Common Factor (GCF) of 786,406 By Common Division

2 786, 406
393, 203

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

Greatest Common Factor of 786,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 786,406 By Matching Biggest Common Factor Method

Now, list down the factors of 786

:

1,2,3,6,131,262,393,786

Now, list down the factors of 406

:

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

Greatest Common Factor

We found the factors 786,406 . The biggest common factor number is the GCF number.
So the greatest common factor 786,406 is 2.

Lets's calculate LCM of 204,268

Lowest Common Multiple of 204,268 using Common Division

2 204, 268
2 102, 134
51, 67

∴ So the LCM of the given numbers is 2 x 2 x 51 x 67 = 13668

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13668

Therefore, the GCF of Fractions 786/204,406/268 is 2/13668

Least Common Multiple of 204,268 with GCF Formula

Least Common Multiple of 204,268 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 204,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(204,268) = 4

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

GCF(204,268) x common factors =4 x 1 = 4

LCM(204,268) = ( 204 × 268 ) / 4

LCM(204,268) = 54672 / 4

LCM(204,268) = 13668


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FAQs on GCF of Fractions of 786/204, 406/268

1. What is the HCF of 786,406?

The HCF of 786,406 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 786/204, 406/268?

Answer: GCF of Numerators as per given numbers 786/204, 406/268 is

GCF of Numerators i.e. for 786,406 is 2

LCM of denominators i.e. for 204,268 is 13668.

Thus, GCF of Fractions is 2/13668.Finally, GCF of Fractions for 786/204, 406/268 is 2/13668.