How to Find GCF of 820/272, 150/638?

GCF of 820/272, 150/638

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 820/272, 150/638 i.e 10/86768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/272, 150/638.

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 820/272,150/638?

Given fractions are 820/272,150/638

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 820/272,150/638, numerators are 820,150

Denominators are 272,638

The GCF of 820,150 is 10 .

LCM of 272,638 is 86768.

The greatest common factor of 820/272,150/638 = [GCF of 820,150]/[LCM of 272,638]= 10/86768

Therefore, the GCF of 820/272,150/638 is 10/86768.

Greatest Common Factor of 820,150

To find the highest common factor of 820,150, we have to find the factors of both numbers and list the highest common factor.

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The HCF of 820,150 is 10.

Lets's calculate GCF of 820,150

Greatest Common Factor (GCF) of 820,150 By Common Division

2	820, 150
5	410, 75
	82, 15

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 820,150 By Matching Biggest Common Factor Method

Now, list down the factors of 820

1,2,4,5,10,20,41,82,164,205,410,820

Now, list down the factors of 150

1,2,3,5,6,10,15,25,30,50,75,150

Greatest Common Factor

We found the factors 820,150 . The biggest common factor number is the GCF number.
So the greatest common factor 820,150 is 10.

Lets's calculate LCM of 272,638

Lowest Common Multiple of 272,638 using Common Division

2	272, 638
	136, 319

∴ So the LCM of the given numbers is 2 x 136 x 319 = 86768

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/86768

Therefore, the GCF of Fractions 820/272,150/638 is 10/86768

Least Common Multiple of 272,638 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 272,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(272,638) = 2

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

GCF(272,638) x common factors =2 x 1 = 2

LCM(272,638) = ( 272 × 638 ) / 2

LCM(272,638) = 173536 / 2

LCM(272,638) = 86768

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FAQs on GCF of Fractions of 820/272, 150/638

1. What is the HCF of 820,150?

The HCF of 820,150 is 10

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 820/272, 150/638?

Answer: GCF of Numerators as per given numbers 820/272, 150/638 is

GCF of Numerators i.e. for 820,150 is 10

LCM of denominators i.e. for 272,638 is 86768.

Thus, GCF of Fractions is 10/86768.Finally, GCF of Fractions for 820/272, 150/638 is 10/86768.