How to Find GCF of 13/228, 20/414, 505/419?

GCF of 13/228, 20/414, 505/419

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 13/228, 20/414, 505/419 i.e 1/6591708 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/228, 20/414, 505/419.

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 13/228,20/414,505/419?

Given fractions are 13/228,20/414,505/419

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 13/228,20/414,505/419, numerators are 13,20,505

Denominators are 228,414,419

The GCF of 13,20,505 is 1 .

LCM of 228,414,419 is 6591708.

The greatest common factor of 13/228,20/414,505/419 = [GCF of 13,20,505]/[LCM of 228,414,419]= 1/6591708

Therefore, the GCF of 13/228,20/414,505/419 is 1/6591708.

Greatest Common Factor of 13,20,505

To find the highest common factor of 13,20,505, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 505 are 1, 5, 101, 505

The HCF of 13,20,505 is 1.

Lets's calculate GCF of 13,20,505

Greatest Common Factor (GCF) of 13,20,505 By Common Division

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

Greatest Common Factor of 13,20,505 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 505

1,5,101,505

Greatest Common Factor

We found the factors 13,20,505 . The biggest common factor number is the GCF number.
So the greatest common factor 13,20,505 is 1.

Lets's calculate LCM of 228,414,419

Lowest Common Multiple of 228,414,419 using Common Division

2	228, 414, 419
3	114, 207, 419
	38, 69, 419

∴ So the LCM of the given numbers is 2 x 3 x 38 x 69 x 419 = 6591708

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6591708

Therefore, the GCF of Fractions 13/228,20/414,505/419 is 1/6591708

Least Common Multiple of 228,414,419 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 228,414,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(228,414,419) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(228,414,419) x common factors =1 x 6 = 6

LCM(228,414,419) = ( 228 × 414 × 419 ) / 6

LCM(228,414,419) = 39550248 / 6

LCM(228,414,419) = 6591708

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FAQs on GCF of Fractions of 13/228, 20/414, 505/419

1. What is the HCF of 13,20,505?

The HCF of 13,20,505 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 13/228, 20/414, 505/419?

Answer: GCF of Numerators as per given numbers 13/228, 20/414, 505/419 is

GCF of Numerators i.e. for 13,20,505 is 1

LCM of denominators i.e. for 228,414,419 is 6591708.

Thus, GCF of Fractions is 1/6591708.Finally, GCF of Fractions for 13/228, 20/414, 505/419 is 1/6591708.