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GCF of 826/66, 812/714

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 826/66, 812/714 i.e 14/7854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 826/66, 812/714.

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 826/66,812/714?

Given fractions are 826/66,812/714

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 826/66,812/714, numerators are 826,812

Denominators are 66,714

The GCF of 826,812 is 14 .

LCM of 66,714 is 7854.

The greatest common factor of 826/66,812/714 = [GCF of 826,812]/[LCM of 66,714]= 14/7854

Therefore, the GCF of 826/66,812/714 is 14/7854.

Greatest Common Factor of 826,812

To find the highest common factor of 826,812, we have to find the factors of both numbers and list the highest common factor.

The factors of 826 are 1, 2, 7, 14, 59, 118, 413, 826

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The HCF of 826,812 is 14.

Lets's calculate GCF of 826,812

Greatest Common Factor (GCF) of 826,812 By Common Division

2 826, 812
7 413, 406
59, 58

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

Greatest Common Factor of 826,812 By Matching Biggest Common Factor Method

Greatest Common Factor of 826,812 By Matching Biggest Common Factor Method

Now, list down the factors of 826

:

1,2,7,14,59,118,413,826

Now, list down the factors of 812

:

1,2,4,7,14,28,29,58,116,203,406,812

Greatest Common Factor

We found the factors 826,812 . The biggest common factor number is the GCF number.
So the greatest common factor 826,812 is 14.

Lets's calculate LCM of 66,714

Lowest Common Multiple of 66,714 using Common Division

2 66, 714
3 33, 357
11, 119

∴ So the LCM of the given numbers is 2 x 3 x 11 x 119 = 7854

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/7854

Therefore, the GCF of Fractions 826/66,812/714 is 14/7854

Least Common Multiple of 66,714 with GCF Formula

Least Common Multiple of 66,714 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 66,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,714) = 6

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

GCF(66,714) x common factors =6 x 1 = 6

LCM(66,714) = ( 66 × 714 ) / 6

LCM(66,714) = 47124 / 6

LCM(66,714) = 7854


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FAQs on GCF of Fractions of 826/66, 812/714

1. What is the HCF of 826,812?

The HCF of 826,812 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 826/66, 812/714?

Answer: GCF of Numerators as per given numbers 826/66, 812/714 is

GCF of Numerators i.e. for 826,812 is 14

LCM of denominators i.e. for 66,714 is 7854.

Thus, GCF of Fractions is 14/7854.Finally, GCF of Fractions for 826/66, 812/714 is 14/7854.