How to Find GCF of 59/69, 430/65, 514/409?

GCF of 59/69, 430/65, 514/409

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 59/69, 430/65, 514/409 i.e 1/1834365 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/69, 430/65, 514/409.

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 59/69,430/65,514/409?

Given fractions are 59/69,430/65,514/409

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 59/69,430/65,514/409, numerators are 59,430,514

Denominators are 69,65,409

The GCF of 59,430,514 is 1 .

LCM of 69,65,409 is 1834365.

The greatest common factor of 59/69,430/65,514/409 = [GCF of 59,430,514]/[LCM of 69,65,409]= 1/1834365

Therefore, the GCF of 59/69,430/65,514/409 is 1/1834365.

Greatest Common Factor of 59,430,514

To find the highest common factor of 59,430,514, we have to find the factors of both numbers and list the highest common factor.

The factors of 59 are 1, 59

The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430

The factors of 514 are 1, 2, 257, 514

The HCF of 59,430,514 is 1.

Lets's calculate GCF of 59,430,514

Greatest Common Factor (GCF) of 59,430,514 By Common Division

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

Greatest Common Factor of 59,430,514 By Matching Biggest Common Factor Method

Now, list down the factors of 59

1,59

Now, list down the factors of 430

1,2,5,10,43,86,215,430

Now, list down the factors of 514

1,2,257,514

Greatest Common Factor

We found the factors 59,430,514 . The biggest common factor number is the GCF number.
So the greatest common factor 59,430,514 is 1.

Lets's calculate LCM of 69,65,409

Lowest Common Multiple of 69,65,409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1834365

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1834365

Therefore, the GCF of Fractions 59/69,430/65,514/409 is 1/1834365

Least Common Multiple of 69,65,409 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 69,65,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,65,409) = 1

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

GCF(69,65,409) x common factors =1 x 1 = 1

LCM(69,65,409) = ( 69 × 65 × 409 ) / 1

LCM(69,65,409) = 1834365 / 1

LCM(69,65,409) = 1834365

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 59/69, 430/65, 514/409

1. What is the HCF of 59,430,514?

The HCF of 59,430,514 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 59/69, 430/65, 514/409?

Answer: GCF of Numerators as per given numbers 59/69, 430/65, 514/409 is

GCF of Numerators i.e. for 59,430,514 is 1

LCM of denominators i.e. for 69,65,409 is 1834365.

Thus, GCF of Fractions is 1/1834365.Finally, GCF of Fractions for 59/69, 430/65, 514/409 is 1/1834365.