How to Find GCF of 14/19, 30/405, 493/719?

GCF of 14/19, 30/405, 493/719

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 14/19, 30/405, 493/719 i.e 1/5532705 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/19, 30/405, 493/719.

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 14/19,30/405,493/719?

Given fractions are 14/19,30/405,493/719

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 14/19,30/405,493/719, numerators are 14,30,493

Denominators are 19,405,719

The GCF of 14,30,493 is 1 .

LCM of 19,405,719 is 5532705.

The greatest common factor of 14/19,30/405,493/719 = [GCF of 14,30,493]/[LCM of 19,405,719]= 1/5532705

Therefore, the GCF of 14/19,30/405,493/719 is 1/5532705.

Greatest Common Factor of 14,30,493

To find the highest common factor of 14,30,493, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 493 are 1, 17, 29, 493

The HCF of 14,30,493 is 1.

Lets's calculate GCF of 14,30,493

Greatest Common Factor (GCF) of 14,30,493 By Common Division

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

Greatest Common Factor of 14,30,493 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 493

1,17,29,493

Greatest Common Factor

We found the factors 14,30,493 . The biggest common factor number is the GCF number.
So the greatest common factor 14,30,493 is 1.

Lets's calculate LCM of 19,405,719

Lowest Common Multiple of 19,405,719 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5532705

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5532705

Therefore, the GCF of Fractions 14/19,30/405,493/719 is 1/5532705

Least Common Multiple of 19,405,719 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 19,405,719 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,405,719) = 1

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

GCF(19,405,719) x common factors =1 x 1 = 1

LCM(19,405,719) = ( 19 × 405 × 719 ) / 1

LCM(19,405,719) = 5532705 / 1

LCM(19,405,719) = 5532705

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FAQs on GCF of Fractions of 14/19, 30/405, 493/719

1. What is the HCF of 14,30,493?

The HCF of 14,30,493 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 14/19, 30/405, 493/719?

Answer: GCF of Numerators as per given numbers 14/19, 30/405, 493/719 is

GCF of Numerators i.e. for 14,30,493 is 1

LCM of denominators i.e. for 19,405,719 is 5532705.

Thus, GCF of Fractions is 1/5532705.Finally, GCF of Fractions for 14/19, 30/405, 493/719 is 1/5532705.