How to Find GCF of 19/321, 66/274, 274/136?

GCF of 19/321, 66/274, 274/136

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 19/321, 66/274, 274/136 i.e 1/5980872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/321, 66/274, 274/136.

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 19/321,66/274,274/136?

Given fractions are 19/321,66/274,274/136

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 19/321,66/274,274/136, numerators are 19,66,274

Denominators are 321,274,136

The GCF of 19,66,274 is 1 .

LCM of 321,274,136 is 5980872.

The greatest common factor of 19/321,66/274,274/136 = [GCF of 19,66,274]/[LCM of 321,274,136]= 1/5980872

Therefore, the GCF of 19/321,66/274,274/136 is 1/5980872.

Greatest Common Factor of 19,66,274

To find the highest common factor of 19,66,274, we have to find the factors of both numbers and list the highest common factor.

The factors of 19 are 1, 19

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 274 are 1, 2, 137, 274

The HCF of 19,66,274 is 1.

Lets's calculate GCF of 19,66,274

Greatest Common Factor (GCF) of 19,66,274 By Common Division

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

Greatest Common Factor of 19,66,274 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 274

1,2,137,274

Greatest Common Factor

We found the factors 19,66,274 . The biggest common factor number is the GCF number.
So the greatest common factor 19,66,274 is 1.

Lets's calculate LCM of 321,274,136

Lowest Common Multiple of 321,274,136 using Common Division

2	321, 274, 136
	321, 137, 68

∴ So the LCM of the given numbers is 2 x 321 x 137 x 68 = 5980872

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5980872

Therefore, the GCF of Fractions 19/321,66/274,274/136 is 1/5980872

Least Common Multiple of 321,274,136 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 321,274,136 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(321,274,136) = 1

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

GCF(321,274,136) x common factors =1 x 2 = 2

LCM(321,274,136) = ( 321 × 274 × 136 ) / 2

LCM(321,274,136) = 11961744 / 2

LCM(321,274,136) = 5980872

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FAQs on GCF of Fractions of 19/321, 66/274, 274/136

1. What is the HCF of 19,66,274?

The HCF of 19,66,274 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 19/321, 66/274, 274/136?

Answer: GCF of Numerators as per given numbers 19/321, 66/274, 274/136 is

GCF of Numerators i.e. for 19,66,274 is 1

LCM of denominators i.e. for 321,274,136 is 5980872.

Thus, GCF of Fractions is 1/5980872.Finally, GCF of Fractions for 19/321, 66/274, 274/136 is 1/5980872.