How to Find GCF of 55/21, 286/89, 231/407?

GCF of 55/21, 286/89, 231/407

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 55/21, 286/89, 231/407 i.e 11/760683 easily. The following is the detailed procedure to determine the greatest common factor of fractions 55/21, 286/89, 231/407.

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 55/21,286/89,231/407?

Given fractions are 55/21,286/89,231/407

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 55/21,286/89,231/407, numerators are 55,286,231

Denominators are 21,89,407

The GCF of 55,286,231 is 11 .

LCM of 21,89,407 is 760683.

The greatest common factor of 55/21,286/89,231/407 = [GCF of 55,286,231]/[LCM of 21,89,407]= 11/760683

Therefore, the GCF of 55/21,286/89,231/407 is 11/760683.

Greatest Common Factor of 55,286,231

To find the highest common factor of 55,286,231, we have to find the factors of both numbers and list the highest common factor.

The factors of 55 are 1, 5, 11, 55

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

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231

The HCF of 55,286,231 is 11.

Lets's calculate GCF of 55,286,231

Greatest Common Factor (GCF) of 55,286,231 By Common Division

11	55, 286, 231
	5, 26, 21

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 55,286,231 By Matching Biggest Common Factor Method

Now, list down the factors of 55

1,5,11,55

Now, list down the factors of 286

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

Now, list down the factors of 231

1,3,7,11,21,33,77,231

Greatest Common Factor

We found the factors 55,286,231 . The biggest common factor number is the GCF number.
So the greatest common factor 55,286,231 is 11.

Lets's calculate LCM of 21,89,407

Lowest Common Multiple of 21,89,407 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 760683

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/760683

Therefore, the GCF of Fractions 55/21,286/89,231/407 is 11/760683

Least Common Multiple of 21,89,407 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 21,89,407 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,89,407) = 1

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

GCF(21,89,407) x common factors =1 x 1 = 1

LCM(21,89,407) = ( 21 × 89 × 407 ) / 1

LCM(21,89,407) = 760683 / 1

LCM(21,89,407) = 760683

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FAQs on GCF of Fractions of 55/21, 286/89, 231/407

1. What is the HCF of 55,286,231?

The HCF of 55,286,231 is 11

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 55/21, 286/89, 231/407?

Answer: GCF of Numerators as per given numbers 55/21, 286/89, 231/407 is

GCF of Numerators i.e. for 55,286,231 is 11

LCM of denominators i.e. for 21,89,407 is 760683.

Thus, GCF of Fractions is 11/760683.Finally, GCF of Fractions for 55/21, 286/89, 231/407 is 11/760683.