How to Find GCF of 19/17, 354/83, 460/258?

GCF of 19/17, 354/83, 460/258

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 19/17, 354/83, 460/258 i.e 1/364038 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/17, 354/83, 460/258.

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 19/17,354/83,460/258?

Given fractions are 19/17,354/83,460/258

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 19/17,354/83,460/258, numerators are 19,354,460

Denominators are 17,83,258

The GCF of 19,354,460 is 1 .

LCM of 17,83,258 is 364038.

The greatest common factor of 19/17,354/83,460/258 = [GCF of 19,354,460]/[LCM of 17,83,258]= 1/364038

Therefore, the GCF of 19/17,354/83,460/258 is 1/364038.

Greatest Common Factor of 19,354,460

To find the highest common factor of 19,354,460, 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 354 are 1, 2, 3, 6, 59, 118, 177, 354

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

The HCF of 19,354,460 is 1.

Lets's calculate GCF of 19,354,460

Greatest Common Factor (GCF) of 19,354,460 By Common Division

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

Greatest Common Factor of 19,354,460 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 354

1,2,3,6,59,118,177,354

Now, list down the factors of 460

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors 19,354,460 . The biggest common factor number is the GCF number.
So the greatest common factor 19,354,460 is 1.

Lets's calculate LCM of 17,83,258

Lowest Common Multiple of 17,83,258 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 364038

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/364038

Therefore, the GCF of Fractions 19/17,354/83,460/258 is 1/364038

Least Common Multiple of 17,83,258 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 17,83,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,83,258) = 1

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

GCF(17,83,258) x common factors =1 x 1 = 1

LCM(17,83,258) = ( 17 × 83 × 258 ) / 1

LCM(17,83,258) = 364038 / 1

LCM(17,83,258) = 364038

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 19/17, 354/83, 460/258

1. What is the HCF of 19,354,460?

The HCF of 19,354,460 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 19/17, 354/83, 460/258?

Answer: GCF of Numerators as per given numbers 19/17, 354/83, 460/258 is

GCF of Numerators i.e. for 19,354,460 is 1

LCM of denominators i.e. for 17,83,258 is 364038.

Thus, GCF of Fractions is 1/364038.Finally, GCF of Fractions for 19/17, 354/83, 460/258 is 1/364038.