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GCF of 827/19, 205/381

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 827/19, 205/381 i.e 1/7239 easily. The following is the detailed procedure to determine the greatest common factor of fractions 827/19, 205/381.

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 827/19,205/381?

Given fractions are 827/19,205/381

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 827/19,205/381, numerators are 827,205

Denominators are 19,381

The GCF of 827,205 is 1 .

LCM of 19,381 is 7239.

The greatest common factor of 827/19,205/381 = [GCF of 827,205]/[LCM of 19,381]= 1/7239

Therefore, the GCF of 827/19,205/381 is 1/7239.

Greatest Common Factor of 827,205

To find the highest common factor of 827,205, we have to find the factors of both numbers and list the highest common factor.

The factors of 827 are 1, 827

The factors of 205 are 1, 5, 41, 205

The HCF of 827,205 is 1.

Lets's calculate GCF of 827,205

Greatest Common Factor (GCF) of 827,205 By Common Division

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

Greatest Common Factor of 827,205 By Matching Biggest Common Factor Method

Greatest Common Factor of 827,205 By Matching Biggest Common Factor Method

Now, list down the factors of 827

:

1,827

Now, list down the factors of 205

:

1,5,41,205

Greatest Common Factor

We found the factors 827,205 . The biggest common factor number is the GCF number.
So the greatest common factor 827,205 is 1.

Lets's calculate LCM of 19,381

Lowest Common Multiple of 19,381 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7239

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7239

Therefore, the GCF of Fractions 827/19,205/381 is 1/7239

Least Common Multiple of 19,381 with GCF Formula

Least Common Multiple of 19,381 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 19,381 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,381) = 1

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

GCF(19,381) x common factors =1 x 1 = 1

LCM(19,381) = ( 19 × 381 ) / 1

LCM(19,381) = 7239 / 1

LCM(19,381) = 7239


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FAQs on GCF of Fractions of 827/19, 205/381

1. What is the HCF of 827,205?

The HCF of 827,205 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 827/19, 205/381?

Answer: GCF of Numerators as per given numbers 827/19, 205/381 is

GCF of Numerators i.e. for 827,205 is 1

LCM of denominators i.e. for 19,381 is 7239.

Thus, GCF of Fractions is 1/7239.Finally, GCF of Fractions for 827/19, 205/381 is 1/7239.