How to Find GCF of 1586/299, 1786/1828?

GCF of 1586/299, 1786/1828

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 1586/299, 1786/1828 i.e 2/546572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1586/299, 1786/1828.

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 1586/299,1786/1828?

Given fractions are 1586/299,1786/1828

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 1586/299,1786/1828, numerators are 1586,1786

Denominators are 299,1828

The GCF of 1586,1786 is 2 .

LCM of 299,1828 is 546572.

The greatest common factor of 1586/299,1786/1828 = [GCF of 1586,1786]/[LCM of 299,1828]= 2/546572

Therefore, the GCF of 1586/299,1786/1828 is 2/546572.

Greatest Common Factor of 1586,1786

To find the highest common factor of 1586,1786, we have to find the factors of both numbers and list the highest common factor.

The factors of 1586 are 1, 2, 13, 26, 61, 122, 793, 1586

The factors of 1786 are 1, 2, 19, 38, 47, 94, 893, 1786

The HCF of 1586,1786 is 2.

Lets's calculate GCF of 1586,1786

Greatest Common Factor (GCF) of 1586,1786 By Common Division

2	1586, 1786
	793, 893

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 1586,1786 By Matching Biggest Common Factor Method

Now, list down the factors of 1586

1,2,13,26,61,122,793,1586

Now, list down the factors of 1786

1,2,19,38,47,94,893,1786

Greatest Common Factor

We found the factors 1586,1786 . The biggest common factor number is the GCF number.
So the greatest common factor 1586,1786 is 2.

Lets's calculate LCM of 299,1828

Lowest Common Multiple of 299,1828 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 546572

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/546572

Therefore, the GCF of Fractions 1586/299,1786/1828 is 2/546572

Least Common Multiple of 299,1828 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 299,1828 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(299,1828) = 1

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

GCF(299,1828) x common factors =1 x 1 = 1

LCM(299,1828) = ( 299 × 1828 ) / 1

LCM(299,1828) = 546572 / 1

LCM(299,1828) = 546572

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1586/299, 1786/1828

1. What is the HCF of 1586,1786?

The HCF of 1586,1786 is 2

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 1586/299, 1786/1828?

Answer: GCF of Numerators as per given numbers 1586/299, 1786/1828 is

GCF of Numerators i.e. for 1586,1786 is 2

LCM of denominators i.e. for 299,1828 is 546572.

Thus, GCF of Fractions is 2/546572.Finally, GCF of Fractions for 1586/299, 1786/1828 is 2/546572.