How to Find GCF of 40/73, 154/30, 180/274?

GCF of 40/73, 154/30, 180/274

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 40/73, 154/30, 180/274 i.e 2/300030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/73, 154/30, 180/274.

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 40/73,154/30,180/274?

Given fractions are 40/73,154/30,180/274

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 40/73,154/30,180/274, numerators are 40,154,180

Denominators are 73,30,274

The GCF of 40,154,180 is 2 .

LCM of 73,30,274 is 300030.

The greatest common factor of 40/73,154/30,180/274 = [GCF of 40,154,180]/[LCM of 73,30,274]= 2/300030

Therefore, the GCF of 40/73,154/30,180/274 is 2/300030.

Greatest Common Factor of 40,154,180

To find the highest common factor of 40,154,180, we have to find the factors of both numbers and list the highest common factor.

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The HCF of 40,154,180 is 2.

Lets's calculate GCF of 40,154,180

Greatest Common Factor (GCF) of 40,154,180 By Common Division

2	40, 154, 180
	20, 77, 90

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 40,154,180 By Matching Biggest Common Factor Method

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 154

1,2,7,11,14,22,77,154

Now, list down the factors of 180

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Greatest Common Factor

We found the factors 40,154,180 . The biggest common factor number is the GCF number.
So the greatest common factor 40,154,180 is 2.

Lets's calculate LCM of 73,30,274

Lowest Common Multiple of 73,30,274 using Common Division

2	73, 30, 274
	73, 15, 137

∴ So the LCM of the given numbers is 2 x 73 x 15 x 137 = 300030

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/300030

Therefore, the GCF of Fractions 40/73,154/30,180/274 is 2/300030

Least Common Multiple of 73,30,274 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 73,30,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(73,30,274) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(73,30,274) x common factors =1 x 2 = 2

LCM(73,30,274) = ( 73 × 30 × 274 ) / 2

LCM(73,30,274) = 600060 / 2

LCM(73,30,274) = 300030

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FAQs on GCF of Fractions of 40/73, 154/30, 180/274

1. What is the HCF of 40,154,180?

The HCF of 40,154,180 is 2

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 40/73, 154/30, 180/274?

Answer: GCF of Numerators as per given numbers 40/73, 154/30, 180/274 is

GCF of Numerators i.e. for 40,154,180 is 2

LCM of denominators i.e. for 73,30,274 is 300030.

Thus, GCF of Fractions is 2/300030.Finally, GCF of Fractions for 40/73, 154/30, 180/274 is 2/300030.