How to Find GCF of 540/74, 210/345?

GCF of 540/74, 210/345

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 540/74, 210/345 i.e 30/25530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/74, 210/345.

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 540/74,210/345?

Given fractions are 540/74,210/345

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 540/74,210/345, numerators are 540,210

Denominators are 74,345

The GCF of 540,210 is 30 .

LCM of 74,345 is 25530.

The greatest common factor of 540/74,210/345 = [GCF of 540,210]/[LCM of 74,345]= 30/25530

Therefore, the GCF of 540/74,210/345 is 30/25530.

Greatest Common Factor of 540,210

To find the highest common factor of 540,210, 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 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 540,210 is 30.

Lets's calculate GCF of 540,210

Greatest Common Factor (GCF) of 540,210 By Common Division

2	540, 210
3	270, 105
5	90, 35
	18, 7

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 540,210 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 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 540,210 . The biggest common factor number is the GCF number.
So the greatest common factor 540,210 is 30.

Lets's calculate LCM of 74,345

Lowest Common Multiple of 74,345 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 25530

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/25530

Therefore, the GCF of Fractions 540/74,210/345 is 30/25530

Least Common Multiple of 74,345 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 74,345 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,345) = 1

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

GCF(74,345) x common factors =1 x 1 = 1

LCM(74,345) = ( 74 × 345 ) / 1

LCM(74,345) = 25530 / 1

LCM(74,345) = 25530

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FAQs on GCF of Fractions of 540/74, 210/345

1. What is the HCF of 540,210?

The HCF of 540,210 is 30

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 540/74, 210/345?

Answer: GCF of Numerators as per given numbers 540/74, 210/345 is

GCF of Numerators i.e. for 540,210 is 30

LCM of denominators i.e. for 74,345 is 25530.

Thus, GCF of Fractions is 30/25530.Finally, GCF of Fractions for 540/74, 210/345 is 30/25530.