How to Find GCF of 500/37, 259/1065?

GCF of 500/37, 259/1065

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 500/37, 259/1065 i.e 1/39405 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/37, 259/1065.

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 500/37,259/1065?

Given fractions are 500/37,259/1065

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 500/37,259/1065, numerators are 500,259

Denominators are 37,1065

The GCF of 500,259 is 1 .

LCM of 37,1065 is 39405.

The greatest common factor of 500/37,259/1065 = [GCF of 500,259]/[LCM of 37,1065]= 1/39405

Therefore, the GCF of 500/37,259/1065 is 1/39405.

Greatest Common Factor of 500,259

To find the highest common factor of 500,259, we have to find the factors of both numbers and list the highest common factor.

The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The factors of 259 are 1, 7, 37, 259

The HCF of 500,259 is 1.

Lets's calculate GCF of 500,259

Greatest Common Factor (GCF) of 500,259 By Common Division

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

Greatest Common Factor of 500,259 By Matching Biggest Common Factor Method

Now, list down the factors of 500

1,2,4,5,10,20,25,50,100,125,250,500

Now, list down the factors of 259

1,7,37,259

Greatest Common Factor

We found the factors 500,259 . The biggest common factor number is the GCF number.
So the greatest common factor 500,259 is 1.

Lets's calculate LCM of 37,1065

Lowest Common Multiple of 37,1065 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 39405

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39405

Therefore, the GCF of Fractions 500/37,259/1065 is 1/39405

Least Common Multiple of 37,1065 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 37,1065 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,1065) = 1

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

GCF(37,1065) x common factors =1 x 1 = 1

LCM(37,1065) = ( 37 × 1065 ) / 1

LCM(37,1065) = 39405 / 1

LCM(37,1065) = 39405

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FAQs on GCF of Fractions of 500/37, 259/1065

1. What is the HCF of 500,259?

The HCF of 500,259 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 500/37, 259/1065?

Answer: GCF of Numerators as per given numbers 500/37, 259/1065 is

GCF of Numerators i.e. for 500,259 is 1

LCM of denominators i.e. for 37,1065 is 39405.

Thus, GCF of Fractions is 1/39405.Finally, GCF of Fractions for 500/37, 259/1065 is 1/39405.