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GCF of 286/40, 269/821

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 286/40, 269/821 i.e 1/32840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/40, 269/821.

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 286/40,269/821?

Given fractions are 286/40,269/821

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 286/40,269/821, numerators are 286,269

Denominators are 40,821

The GCF of 286,269 is 1 .

LCM of 40,821 is 32840.

The greatest common factor of 286/40,269/821 = [GCF of 286,269]/[LCM of 40,821]= 1/32840

Therefore, the GCF of 286/40,269/821 is 1/32840.

Greatest Common Factor of 286,269

To find the highest common factor of 286,269, we have to find the factors of both numbers and list the highest common factor.

The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286

The factors of 269 are 1, 269

The HCF of 286,269 is 1.

Lets's calculate GCF of 286,269

Greatest Common Factor (GCF) of 286,269 By Common Division

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

Greatest Common Factor of 286,269 By Matching Biggest Common Factor Method

Greatest Common Factor of 286,269 By Matching Biggest Common Factor Method

Now, list down the factors of 286

:

1,2,11,13,22,26,143,286

Now, list down the factors of 269

:

1,269

Greatest Common Factor

We found the factors 286,269 . The biggest common factor number is the GCF number.
So the greatest common factor 286,269 is 1.

Lets's calculate LCM of 40,821

Lowest Common Multiple of 40,821 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 32840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32840

Therefore, the GCF of Fractions 286/40,269/821 is 1/32840

Least Common Multiple of 40,821 with GCF Formula

Least Common Multiple of 40,821 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 40,821 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,821) = 1

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

GCF(40,821) x common factors =1 x 1 = 1

LCM(40,821) = ( 40 × 821 ) / 1

LCM(40,821) = 32840 / 1

LCM(40,821) = 32840


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FAQs on GCF of Fractions of 286/40, 269/821

1. What is the HCF of 286,269?

The HCF of 286,269 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 286/40, 269/821?

Answer: GCF of Numerators as per given numbers 286/40, 269/821 is

GCF of Numerators i.e. for 286,269 is 1

LCM of denominators i.e. for 40,821 is 32840.

Thus, GCF of Fractions is 1/32840.Finally, GCF of Fractions for 286/40, 269/821 is 1/32840.