How to Find GCF of 219/932, 540/973?

GCF of 219/932, 540/973

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 219/932, 540/973 i.e 3/906836 easily. The following is the detailed procedure to determine the greatest common factor of fractions 219/932, 540/973.

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 219/932,540/973?

Given fractions are 219/932,540/973

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 219/932,540/973, numerators are 219,540

Denominators are 932,973

The GCF of 219,540 is 3 .

LCM of 932,973 is 906836.

The greatest common factor of 219/932,540/973 = [GCF of 219,540]/[LCM of 932,973]= 3/906836

Therefore, the GCF of 219/932,540/973 is 3/906836.

Greatest Common Factor of 219,540

To find the highest common factor of 219,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 219 are 1, 3, 73, 219

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 219,540 is 3.

Lets's calculate GCF of 219,540

Greatest Common Factor (GCF) of 219,540 By Common Division

3	219, 540
	73, 180

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 219,540 By Matching Biggest Common Factor Method

Now, list down the factors of 219

1,3,73,219

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 219,540 . The biggest common factor number is the GCF number.
So the greatest common factor 219,540 is 3.

Lets's calculate LCM of 932,973

Lowest Common Multiple of 932,973 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 906836

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/906836

Therefore, the GCF of Fractions 219/932,540/973 is 3/906836

Least Common Multiple of 932,973 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 932,973 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(932,973) = 1

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

GCF(932,973) x common factors =1 x 1 = 1

LCM(932,973) = ( 932 × 973 ) / 1

LCM(932,973) = 906836 / 1

LCM(932,973) = 906836

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FAQs on GCF of Fractions of 219/932, 540/973

1. What is the HCF of 219,540?

The HCF of 219,540 is 3

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 219/932, 540/973?

Answer: GCF of Numerators as per given numbers 219/932, 540/973 is

GCF of Numerators i.e. for 219,540 is 3

LCM of denominators i.e. for 932,973 is 906836.

Thus, GCF of Fractions is 3/906836.Finally, GCF of Fractions for 219/932, 540/973 is 3/906836.