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GCF of 822/827, 208/767

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 822/827, 208/767 i.e 2/634309 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/827, 208/767.

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 822/827,208/767?

Given fractions are 822/827,208/767

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 822/827,208/767, numerators are 822,208

Denominators are 827,767

The GCF of 822,208 is 2 .

LCM of 827,767 is 634309.

The greatest common factor of 822/827,208/767 = [GCF of 822,208]/[LCM of 827,767]= 2/634309

Therefore, the GCF of 822/827,208/767 is 2/634309.

Greatest Common Factor of 822,208

To find the highest common factor of 822,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 822,208 is 2.

Lets's calculate GCF of 822,208

Greatest Common Factor (GCF) of 822,208 By Common Division

2 822, 208
411, 104

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

Greatest Common Factor of 822,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 822,208 By Matching Biggest Common Factor Method

Now, list down the factors of 822

:

1,2,3,6,137,274,411,822

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 822,208 . The biggest common factor number is the GCF number.
So the greatest common factor 822,208 is 2.

Lets's calculate LCM of 827,767

Lowest Common Multiple of 827,767 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 634309

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/634309

Therefore, the GCF of Fractions 822/827,208/767 is 2/634309

Least Common Multiple of 827,767 with GCF Formula

Least Common Multiple of 827,767 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 827,767 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(827,767) = 1

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

GCF(827,767) x common factors =1 x 1 = 1

LCM(827,767) = ( 827 × 767 ) / 1

LCM(827,767) = 634309 / 1

LCM(827,767) = 634309


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FAQs on GCF of Fractions of 822/827, 208/767

1. What is the HCF of 822,208?

The HCF of 822,208 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 822/827, 208/767?

Answer: GCF of Numerators as per given numbers 822/827, 208/767 is

GCF of Numerators i.e. for 822,208 is 2

LCM of denominators i.e. for 827,767 is 634309.

Thus, GCF of Fractions is 2/634309.Finally, GCF of Fractions for 822/827, 208/767 is 2/634309.