How to Find GCF of 39/123, 50/538, 410/784?

GCF of 39/123, 50/538, 410/784

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 39/123, 50/538, 410/784 i.e 1/25940208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/123, 50/538, 410/784.

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 39/123,50/538,410/784?

Given fractions are 39/123,50/538,410/784

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 39/123,50/538,410/784, numerators are 39,50,410

Denominators are 123,538,784

The GCF of 39,50,410 is 1 .

LCM of 123,538,784 is 25940208.

The greatest common factor of 39/123,50/538,410/784 = [GCF of 39,50,410]/[LCM of 123,538,784]= 1/25940208

Therefore, the GCF of 39/123,50/538,410/784 is 1/25940208.

Greatest Common Factor of 39,50,410

To find the highest common factor of 39,50,410, we have to find the factors of both numbers and list the highest common factor.

The factors of 39 are 1, 3, 13, 39

The factors of 50 are 1, 2, 5, 10, 25, 50

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410

The HCF of 39,50,410 is 1.

Lets's calculate GCF of 39,50,410

Greatest Common Factor (GCF) of 39,50,410 By Common Division

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

Greatest Common Factor of 39,50,410 By Matching Biggest Common Factor Method

Now, list down the factors of 39

1,3,13,39

Now, list down the factors of 50

1,2,5,10,25,50

Now, list down the factors of 410

1,2,5,10,41,82,205,410

Greatest Common Factor

We found the factors 39,50,410 . The biggest common factor number is the GCF number.
So the greatest common factor 39,50,410 is 1.

Lets's calculate LCM of 123,538,784

Lowest Common Multiple of 123,538,784 using Common Division

2	123, 538, 784
	123, 269, 392

∴ So the LCM of the given numbers is 2 x 123 x 269 x 392 = 25940208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25940208

Therefore, the GCF of Fractions 39/123,50/538,410/784 is 1/25940208

Least Common Multiple of 123,538,784 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 123,538,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(123,538,784) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(123,538,784) x common factors =1 x 2 = 2

LCM(123,538,784) = ( 123 × 538 × 784 ) / 2

LCM(123,538,784) = 51880416 / 2

LCM(123,538,784) = 25940208

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FAQs on GCF of Fractions of 39/123, 50/538, 410/784

1. What is the HCF of 39,50,410?

The HCF of 39,50,410 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 39/123, 50/538, 410/784?

Answer: GCF of Numerators as per given numbers 39/123, 50/538, 410/784 is

GCF of Numerators i.e. for 39,50,410 is 1

LCM of denominators i.e. for 123,538,784 is 25940208.

Thus, GCF of Fractions is 1/25940208.Finally, GCF of Fractions for 39/123, 50/538, 410/784 is 1/25940208.