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GCF of 822/65, 257/629

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 822/65, 257/629 i.e 1/40885 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/65, 257/629.

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 822/65,257/629?

Given fractions are 822/65,257/629

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 822/65,257/629, numerators are 822,257

Denominators are 65,629

The GCF of 822,257 is 1 .

LCM of 65,629 is 40885.

The greatest common factor of 822/65,257/629 = [GCF of 822,257]/[LCM of 65,629]= 1/40885

Therefore, the GCF of 822/65,257/629 is 1/40885.

Greatest Common Factor of 822,257

To find the highest common factor of 822,257, 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 257 are 1, 257

The HCF of 822,257 is 1.

Lets's calculate GCF of 822,257

Greatest Common Factor (GCF) of 822,257 By Common Division

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

Greatest Common Factor of 822,257 By Matching Biggest Common Factor Method

Greatest Common Factor of 822,257 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 257

:

1,257

Greatest Common Factor

We found the factors 822,257 . The biggest common factor number is the GCF number.
So the greatest common factor 822,257 is 1.

Lets's calculate LCM of 65,629

Lowest Common Multiple of 65,629 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 40885

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40885

Therefore, the GCF of Fractions 822/65,257/629 is 1/40885

Least Common Multiple of 65,629 with GCF Formula

Least Common Multiple of 65,629 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 65,629 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,629) = 1

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

GCF(65,629) x common factors =1 x 1 = 1

LCM(65,629) = ( 65 × 629 ) / 1

LCM(65,629) = 40885 / 1

LCM(65,629) = 40885


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FAQs on GCF of Fractions of 822/65, 257/629

1. What is the HCF of 822,257?

The HCF of 822,257 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 822/65, 257/629?

Answer: GCF of Numerators as per given numbers 822/65, 257/629 is

GCF of Numerators i.e. for 822,257 is 1

LCM of denominators i.e. for 65,629 is 40885.

Thus, GCF of Fractions is 1/40885.Finally, GCF of Fractions for 822/65, 257/629 is 1/40885.