How to Find GCF of 426/173, 540/135?

GCF of 426/173, 540/135

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 426/173, 540/135 i.e 6/23355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 426/173, 540/135.

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 426/173,540/135?

Given fractions are 426/173,540/135

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 426/173,540/135, numerators are 426,540

Denominators are 173,135

The GCF of 426,540 is 6 .

LCM of 173,135 is 23355.

The greatest common factor of 426/173,540/135 = [GCF of 426,540]/[LCM of 173,135]= 6/23355

Therefore, the GCF of 426/173,540/135 is 6/23355.

Greatest Common Factor of 426,540

To find the highest common factor of 426,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426

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 426,540 is 6.

Lets's calculate GCF of 426,540

Greatest Common Factor (GCF) of 426,540 By Common Division

2	426, 540
3	213, 270
	71, 90

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 426,540 By Matching Biggest Common Factor Method

Now, list down the factors of 426

1,2,3,6,71,142,213,426

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 426,540 . The biggest common factor number is the GCF number.
So the greatest common factor 426,540 is 6.

Lets's calculate LCM of 173,135

Lowest Common Multiple of 173,135 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 23355

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/23355

Therefore, the GCF of Fractions 426/173,540/135 is 6/23355

Least Common Multiple of 173,135 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 173,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(173,135) = 1

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

GCF(173,135) x common factors =1 x 1 = 1

LCM(173,135) = ( 173 × 135 ) / 1

LCM(173,135) = 23355 / 1

LCM(173,135) = 23355

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FAQs on GCF of Fractions of 426/173, 540/135

1. What is the HCF of 426,540?

The HCF of 426,540 is 6

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 426/173, 540/135?

Answer: GCF of Numerators as per given numbers 426/173, 540/135 is

GCF of Numerators i.e. for 426,540 is 6

LCM of denominators i.e. for 173,135 is 23355.

Thus, GCF of Fractions is 6/23355.Finally, GCF of Fractions for 426/173, 540/135 is 6/23355.