How to Find GCF of 540/725, 774/469?

GCF of 540/725, 774/469

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 540/725, 774/469 i.e 18/340025 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/725, 774/469.

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 540/725,774/469?

Given fractions are 540/725,774/469

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 540/725,774/469, numerators are 540,774

Denominators are 725,469

The GCF of 540,774 is 18 .

LCM of 725,469 is 340025.

The greatest common factor of 540/725,774/469 = [GCF of 540,774]/[LCM of 725,469]= 18/340025

Therefore, the GCF of 540/725,774/469 is 18/340025.

Greatest Common Factor of 540,774

To find the highest common factor of 540,774, we have to find the factors of both numbers and list the highest common factor.

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 factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774

The HCF of 540,774 is 18.

Lets's calculate GCF of 540,774

Greatest Common Factor (GCF) of 540,774 By Common Division

2	540, 774
3	270, 387
3	90, 129
	30, 43

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 540,774 By Matching Biggest Common Factor Method

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

Now, list down the factors of 774

1,2,3,6,9,18,43,86,129,258,387,774

Greatest Common Factor

We found the factors 540,774 . The biggest common factor number is the GCF number.
So the greatest common factor 540,774 is 18.

Lets's calculate LCM of 725,469

Lowest Common Multiple of 725,469 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 340025

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/340025

Therefore, the GCF of Fractions 540/725,774/469 is 18/340025

Least Common Multiple of 725,469 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 725,469 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(725,469) = 1

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

GCF(725,469) x common factors =1 x 1 = 1

LCM(725,469) = ( 725 × 469 ) / 1

LCM(725,469) = 340025 / 1

LCM(725,469) = 340025

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FAQs on GCF of Fractions of 540/725, 774/469

1. What is the HCF of 540,774?

The HCF of 540,774 is 18

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 540/725, 774/469?

Answer: GCF of Numerators as per given numbers 540/725, 774/469 is

GCF of Numerators i.e. for 540,774 is 18

LCM of denominators i.e. for 725,469 is 340025.

Thus, GCF of Fractions is 18/340025.Finally, GCF of Fractions for 540/725, 774/469 is 18/340025.