How to Find GCF of 227/400, 3086/728?

GCF of 227/400, 3086/728

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 227/400, 3086/728 i.e 1/36400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 227/400, 3086/728.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 227/400,3086/728?

Given fractions are 227/400,3086/728

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 227/400,3086/728, numerators are 227,3086

Denominators are 400,728

The GCF of 227,3086 is 1 .

LCM of 400,728 is 36400.

The greatest common factor of 227/400,3086/728 = [GCF of 227,3086]/[LCM of 400,728]= 1/36400

Therefore, the GCF of 227/400,3086/728 is 1/36400.

Greatest Common Factor of 227,3086

To find the highest common factor of 227,3086, we have to find the factors of both numbers and list the highest common factor.

The factors of 227 are 1, 227

The factors of 3086 are 1, 2, 1543, 3086

The HCF of 227,3086 is 1.

Lets's calculate GCF of 227,3086

Greatest Common Factor (GCF) of 227,3086 By Common Division

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

Greatest Common Factor of 227,3086 By Matching Biggest Common Factor Method

Now, list down the factors of 227

1,227

Now, list down the factors of 3086

1,2,1543,3086

Greatest Common Factor

We found the factors 227,3086 . The biggest common factor number is the GCF number.
So the greatest common factor 227,3086 is 1.

Lets's calculate LCM of 400,728

Lowest Common Multiple of 400,728 using Common Division

2	400, 728
2	200, 364
2	100, 182
	50, 91

∴ So the LCM of the given numbers is 2 x 2 x 2 x 50 x 91 = 36400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/36400

Therefore, the GCF of Fractions 227/400,3086/728 is 1/36400

Least Common Multiple of 400,728 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 400,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,728) = 8

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

GCF(400,728) x common factors =8 x 1 = 8

LCM(400,728) = ( 400 × 728 ) / 8

LCM(400,728) = 291200 / 8

LCM(400,728) = 36400

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FAQs on GCF of Fractions of 227/400, 3086/728

1. What is the HCF of 227,3086?

The HCF of 227,3086 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 227/400, 3086/728?

Answer: GCF of Numerators as per given numbers 227/400, 3086/728 is

GCF of Numerators i.e. for 227,3086 is 1

LCM of denominators i.e. for 400,728 is 36400.

Thus, GCF of Fractions is 1/36400.Finally, GCF of Fractions for 227/400, 3086/728 is 1/36400.