How to Find GCF of 75/31, 50/20, 142/638?

GCF of 75/31, 50/20, 142/638

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 75/31, 50/20, 142/638 i.e 1/197780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/31, 50/20, 142/638.

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 75/31,50/20,142/638?

Given fractions are 75/31,50/20,142/638

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 75/31,50/20,142/638, numerators are 75,50,142

Denominators are 31,20,638

The GCF of 75,50,142 is 1 .

LCM of 31,20,638 is 197780.

The greatest common factor of 75/31,50/20,142/638 = [GCF of 75,50,142]/[LCM of 31,20,638]= 1/197780

Therefore, the GCF of 75/31,50/20,142/638 is 1/197780.

Greatest Common Factor of 75,50,142

To find the highest common factor of 75,50,142, we have to find the factors of both numbers and list the highest common factor.

The factors of 75 are 1, 3, 5, 15, 25, 75

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

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

The HCF of 75,50,142 is 1.

Lets's calculate GCF of 75,50,142

Greatest Common Factor (GCF) of 75,50,142 By Common Division

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

Greatest Common Factor of 75,50,142 By Matching Biggest Common Factor Method

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 50

1,2,5,10,25,50

Now, list down the factors of 142

1,2,71,142

Greatest Common Factor

We found the factors 75,50,142 . The biggest common factor number is the GCF number.
So the greatest common factor 75,50,142 is 1.

Lets's calculate LCM of 31,20,638

Lowest Common Multiple of 31,20,638 using Common Division

2	31, 20, 638
	31, 10, 319

∴ So the LCM of the given numbers is 2 x 31 x 10 x 319 = 197780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/197780

Therefore, the GCF of Fractions 75/31,50/20,142/638 is 1/197780

Least Common Multiple of 31,20,638 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 31,20,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,20,638) = 1

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

GCF(31,20,638) x common factors =1 x 2 = 2

LCM(31,20,638) = ( 31 × 20 × 638 ) / 2

LCM(31,20,638) = 395560 / 2

LCM(31,20,638) = 197780

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FAQs on GCF of Fractions of 75/31, 50/20, 142/638

1. What is the HCF of 75,50,142?

The HCF of 75,50,142 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 75/31, 50/20, 142/638?

Answer: GCF of Numerators as per given numbers 75/31, 50/20, 142/638 is

GCF of Numerators i.e. for 75,50,142 is 1

LCM of denominators i.e. for 31,20,638 is 197780.

Thus, GCF of Fractions is 1/197780.Finally, GCF of Fractions for 75/31, 50/20, 142/638 is 1/197780.