How to Find GCF of 59/31, 31/34, 589/219?

GCF of 59/31, 31/34, 589/219

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 59/31, 31/34, 589/219 i.e 1/230826 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/31, 31/34, 589/219.

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 59/31,31/34,589/219?

Given fractions are 59/31,31/34,589/219

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 59/31,31/34,589/219, numerators are 59,31,589

Denominators are 31,34,219

The GCF of 59,31,589 is 1 .

LCM of 31,34,219 is 230826.

The greatest common factor of 59/31,31/34,589/219 = [GCF of 59,31,589]/[LCM of 31,34,219]= 1/230826

Therefore, the GCF of 59/31,31/34,589/219 is 1/230826.

Greatest Common Factor of 59,31,589

To find the highest common factor of 59,31,589, we have to find the factors of both numbers and list the highest common factor.

The factors of 59 are 1, 59

The factors of 31 are 1, 31

The factors of 589 are 1, 19, 31, 589

The HCF of 59,31,589 is 1.

Lets's calculate GCF of 59,31,589

Greatest Common Factor (GCF) of 59,31,589 By Common Division

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

Greatest Common Factor of 59,31,589 By Matching Biggest Common Factor Method

Now, list down the factors of 59

1,59

Now, list down the factors of 31

1,31

Now, list down the factors of 589

1,19,31,589

Greatest Common Factor

We found the factors 59,31,589 . The biggest common factor number is the GCF number.
So the greatest common factor 59,31,589 is 1.

Lets's calculate LCM of 31,34,219

Lowest Common Multiple of 31,34,219 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 230826

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/230826

Therefore, the GCF of Fractions 59/31,31/34,589/219 is 1/230826

Least Common Multiple of 31,34,219 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 31,34,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,34,219) = 1

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

GCF(31,34,219) x common factors =1 x 1 = 1

LCM(31,34,219) = ( 31 × 34 × 219 ) / 1

LCM(31,34,219) = 230826 / 1

LCM(31,34,219) = 230826

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FAQs on GCF of Fractions of 59/31, 31/34, 589/219

1. What is the HCF of 59,31,589?

The HCF of 59,31,589 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 59/31, 31/34, 589/219?

Answer: GCF of Numerators as per given numbers 59/31, 31/34, 589/219 is

GCF of Numerators i.e. for 59,31,589 is 1

LCM of denominators i.e. for 31,34,219 is 230826.

Thus, GCF of Fractions is 1/230826.Finally, GCF of Fractions for 59/31, 31/34, 589/219 is 1/230826.