How to Find GCF of 540/402, 589/466?

GCF of 540/402, 589/466

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 540/402, 589/466 i.e 1/93666 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/402, 589/466.

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 540/402,589/466?

Given fractions are 540/402,589/466

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 540/402,589/466, numerators are 540,589

Denominators are 402,466

The GCF of 540,589 is 1 .

LCM of 402,466 is 93666.

The greatest common factor of 540/402,589/466 = [GCF of 540,589]/[LCM of 402,466]= 1/93666

Therefore, the GCF of 540/402,589/466 is 1/93666.

Greatest Common Factor of 540,589

To find the highest common factor of 540,589, 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 589 are 1, 19, 31, 589

The HCF of 540,589 is 1.

Lets's calculate GCF of 540,589

Greatest Common Factor (GCF) of 540,589 By Common Division

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

Greatest Common Factor of 540,589 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 589

1,19,31,589

Greatest Common Factor

We found the factors 540,589 . The biggest common factor number is the GCF number.
So the greatest common factor 540,589 is 1.

Lets's calculate LCM of 402,466

Lowest Common Multiple of 402,466 using Common Division

2	402, 466
	201, 233

∴ So the LCM of the given numbers is 2 x 201 x 233 = 93666

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93666

Therefore, the GCF of Fractions 540/402,589/466 is 1/93666

Least Common Multiple of 402,466 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 402,466 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(402,466) = 2

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

GCF(402,466) x common factors =2 x 1 = 2

LCM(402,466) = ( 402 × 466 ) / 2

LCM(402,466) = 187332 / 2

LCM(402,466) = 93666

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FAQs on GCF of Fractions of 540/402, 589/466

1. What is the HCF of 540,589?

The HCF of 540,589 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 540/402, 589/466?

Answer: GCF of Numerators as per given numbers 540/402, 589/466 is

GCF of Numerators i.e. for 540,589 is 1

LCM of denominators i.e. for 402,466 is 93666.

Thus, GCF of Fractions is 1/93666.Finally, GCF of Fractions for 540/402, 589/466 is 1/93666.