How to Find GCF of 15/19, 49/21, 310/23?

GCF of 15/19, 49/21, 310/23

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 15/19, 49/21, 310/23 i.e 1/9177 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/19, 49/21, 310/23.

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 15/19,49/21,310/23?

Given fractions are 15/19,49/21,310/23

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 15/19,49/21,310/23, numerators are 15,49,310

Denominators are 19,21,23

The GCF of 15,49,310 is 1 .

LCM of 19,21,23 is 9177.

The greatest common factor of 15/19,49/21,310/23 = [GCF of 15,49,310]/[LCM of 19,21,23]= 1/9177

Therefore, the GCF of 15/19,49/21,310/23 is 1/9177.

Greatest Common Factor of 15,49,310

To find the highest common factor of 15,49,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 15 are 1, 3, 5, 15

The factors of 49 are 1, 7, 49

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 15,49,310 is 1.

Lets's calculate GCF of 15,49,310

Greatest Common Factor (GCF) of 15,49,310 By Common Division

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

Greatest Common Factor of 15,49,310 By Matching Biggest Common Factor Method

Now, list down the factors of 15

1,3,5,15

Now, list down the factors of 49

1,7,49

Now, list down the factors of 310

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 15,49,310 . The biggest common factor number is the GCF number.
So the greatest common factor 15,49,310 is 1.

Lets's calculate LCM of 19,21,23

Lowest Common Multiple of 19,21,23 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9177

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9177

Therefore, the GCF of Fractions 15/19,49/21,310/23 is 1/9177

Least Common Multiple of 19,21,23 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 19,21,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,21,23) = 1

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

GCF(19,21,23) x common factors =1 x 1 = 1

LCM(19,21,23) = ( 19 × 21 × 23 ) / 1

LCM(19,21,23) = 9177 / 1

LCM(19,21,23) = 9177

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 15/19, 49/21, 310/23

1. What is the HCF of 15,49,310?

The HCF of 15,49,310 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 15/19, 49/21, 310/23?

Answer: GCF of Numerators as per given numbers 15/19, 49/21, 310/23 is

GCF of Numerators i.e. for 15,49,310 is 1

LCM of denominators i.e. for 19,21,23 is 9177.

Thus, GCF of Fractions is 1/9177.Finally, GCF of Fractions for 15/19, 49/21, 310/23 is 1/9177.