How to Find GCF of 19/269, 34/412, 513/628?

GCF of 19/269, 34/412, 513/628

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 19/269, 34/412, 513/628 i.e 1/17399996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/269, 34/412, 513/628.

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 19/269,34/412,513/628?

Given fractions are 19/269,34/412,513/628

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 19/269,34/412,513/628, numerators are 19,34,513

Denominators are 269,412,628

The GCF of 19,34,513 is 1 .

LCM of 269,412,628 is 17399996.

The greatest common factor of 19/269,34/412,513/628 = [GCF of 19,34,513]/[LCM of 269,412,628]= 1/17399996

Therefore, the GCF of 19/269,34/412,513/628 is 1/17399996.

Greatest Common Factor of 19,34,513

To find the highest common factor of 19,34,513, 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 34 are 1, 2, 17, 34

The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513

The HCF of 19,34,513 is 1.

Lets's calculate GCF of 19,34,513

Greatest Common Factor (GCF) of 19,34,513 By Common Division

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

Greatest Common Factor of 19,34,513 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 513

1,3,9,19,27,57,171,513

Greatest Common Factor

We found the factors 19,34,513 . The biggest common factor number is the GCF number.
So the greatest common factor 19,34,513 is 1.

Lets's calculate LCM of 269,412,628

Lowest Common Multiple of 269,412,628 using Common Division

2	269, 412, 628
2	269, 206, 314
	269, 103, 157

∴ So the LCM of the given numbers is 2 x 2 x 269 x 103 x 157 = 17399996

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17399996

Therefore, the GCF of Fractions 19/269,34/412,513/628 is 1/17399996

Least Common Multiple of 269,412,628 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 269,412,628 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(269,412,628) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(269,412,628) x common factors =1 x 4 = 4

LCM(269,412,628) = ( 269 × 412 × 628 ) / 4

LCM(269,412,628) = 69599984 / 4

LCM(269,412,628) = 17399996

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 19/269, 34/412, 513/628

1. What is the HCF of 19,34,513?

The HCF of 19,34,513 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 19/269, 34/412, 513/628?

Answer: GCF of Numerators as per given numbers 19/269, 34/412, 513/628 is

GCF of Numerators i.e. for 19,34,513 is 1

LCM of denominators i.e. for 269,412,628 is 17399996.

Thus, GCF of Fractions is 1/17399996.Finally, GCF of Fractions for 19/269, 34/412, 513/628 is 1/17399996.