How to Find GCF of 19/14, 71/27, 646/10?

GCF of 19/14, 71/27, 646/10

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 19/14, 71/27, 646/10 i.e 1/1890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/14, 71/27, 646/10.

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 19/14,71/27,646/10?

Given fractions are 19/14,71/27,646/10

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 19/14,71/27,646/10, numerators are 19,71,646

Denominators are 14,27,10

The GCF of 19,71,646 is 1 .

LCM of 14,27,10 is 1890.

The greatest common factor of 19/14,71/27,646/10 = [GCF of 19,71,646]/[LCM of 14,27,10]= 1/1890

Therefore, the GCF of 19/14,71/27,646/10 is 1/1890.

Greatest Common Factor of 19,71,646

To find the highest common factor of 19,71,646, 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 71 are 1, 71

The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646

The HCF of 19,71,646 is 1.

Lets's calculate GCF of 19,71,646

Greatest Common Factor (GCF) of 19,71,646 By Common Division

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

Greatest Common Factor of 19,71,646 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 71

1,71

Now, list down the factors of 646

1,2,17,19,34,38,323,646

Greatest Common Factor

We found the factors 19,71,646 . The biggest common factor number is the GCF number.
So the greatest common factor 19,71,646 is 1.

Lets's calculate LCM of 14,27,10

Lowest Common Multiple of 14,27,10 using Common Division

2	14, 27, 10
	7, 27, 5

∴ So the LCM of the given numbers is 2 x 7 x 27 x 5 = 1890

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1890

Therefore, the GCF of Fractions 19/14,71/27,646/10 is 1/1890

Least Common Multiple of 14,27,10 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 14,27,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,27,10) = 1

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

GCF(14,27,10) x common factors =1 x 2 = 2

LCM(14,27,10) = ( 14 × 27 × 10 ) / 2

LCM(14,27,10) = 3780 / 2

LCM(14,27,10) = 1890

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 19/14, 71/27, 646/10

1. What is the HCF of 19,71,646?

The HCF of 19,71,646 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 19/14, 71/27, 646/10?

Answer: GCF of Numerators as per given numbers 19/14, 71/27, 646/10 is

GCF of Numerators i.e. for 19,71,646 is 1

LCM of denominators i.e. for 14,27,10 is 1890.

Thus, GCF of Fractions is 1/1890.Finally, GCF of Fractions for 19/14, 71/27, 646/10 is 1/1890.