How to Find GCF of 142/580, 2109/6201?

GCF of 142/580, 2109/6201

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 142/580, 2109/6201 i.e 1/3596580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/580, 2109/6201.

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 142/580,2109/6201?

Given fractions are 142/580,2109/6201

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 142/580,2109/6201, numerators are 142,2109

Denominators are 580,6201

The GCF of 142,2109 is 1 .

LCM of 580,6201 is 3596580.

The greatest common factor of 142/580,2109/6201 = [GCF of 142,2109]/[LCM of 580,6201]= 1/3596580

Therefore, the GCF of 142/580,2109/6201 is 1/3596580.

Greatest Common Factor of 142,2109

To find the highest common factor of 142,2109, we have to find the factors of both numbers and list the highest common factor.

The factors of 142 are 1, 2, 71, 142

The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109

The HCF of 142,2109 is 1.

Lets's calculate GCF of 142,2109

Greatest Common Factor (GCF) of 142,2109 By Common Division

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

Greatest Common Factor of 142,2109 By Matching Biggest Common Factor Method

Now, list down the factors of 142

1,2,71,142

Now, list down the factors of 2109

1,3,19,37,57,111,703,2109

Greatest Common Factor

We found the factors 142,2109 . The biggest common factor number is the GCF number.
So the greatest common factor 142,2109 is 1.

Lets's calculate LCM of 580,6201

Lowest Common Multiple of 580,6201 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3596580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3596580

Therefore, the GCF of Fractions 142/580,2109/6201 is 1/3596580

Least Common Multiple of 580,6201 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 580,6201 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(580,6201) = 1

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

GCF(580,6201) x common factors =1 x 1 = 1

LCM(580,6201) = ( 580 × 6201 ) / 1

LCM(580,6201) = 3596580 / 1

LCM(580,6201) = 3596580

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FAQs on GCF of Fractions of 142/580, 2109/6201

1. What is the HCF of 142,2109?

The HCF of 142,2109 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 142/580, 2109/6201?

Answer: GCF of Numerators as per given numbers 142/580, 2109/6201 is

GCF of Numerators i.e. for 142,2109 is 1

LCM of denominators i.e. for 580,6201 is 3596580.

Thus, GCF of Fractions is 1/3596580.Finally, GCF of Fractions for 142/580, 2109/6201 is 1/3596580.