How to Find GCF of 60/61, 28/28, 406/413?

GCF of 60/61, 28/28, 406/413

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 60/61, 28/28, 406/413 i.e 2/100772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/61, 28/28, 406/413.

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 60/61,28/28,406/413?

Given fractions are 60/61,28/28,406/413

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 60/61,28/28,406/413, numerators are 60,28,406

Denominators are 61,28,413

The GCF of 60,28,406 is 2 .

LCM of 61,28,413 is 100772.

The greatest common factor of 60/61,28/28,406/413 = [GCF of 60,28,406]/[LCM of 61,28,413]= 2/100772

Therefore, the GCF of 60/61,28/28,406/413 is 2/100772.

Greatest Common Factor of 60,28,406

To find the highest common factor of 60,28,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 60,28,406 is 2.

Lets's calculate GCF of 60,28,406

Greatest Common Factor (GCF) of 60,28,406 By Common Division

2	60, 28, 406
	30, 14, 203

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 60,28,406 By Matching Biggest Common Factor Method

Now, list down the factors of 60

1,2,3,4,5,6,10,12,15,20,30,60

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 60,28,406 . The biggest common factor number is the GCF number.
So the greatest common factor 60,28,406 is 2.

Lets's calculate LCM of 61,28,413

Lowest Common Multiple of 61,28,413 using Common Division

7	61, 28, 413
	61, 4, 59

∴ So the LCM of the given numbers is 7 x 61 x 4 x 59 = 100772

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/100772

Therefore, the GCF of Fractions 60/61,28/28,406/413 is 2/100772

Least Common Multiple of 61,28,413 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 61,28,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(61,28,413) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(61,28,413) x common factors =1 x 7 = 7

LCM(61,28,413) = ( 61 × 28 × 413 ) / 7

LCM(61,28,413) = 705404 / 7

LCM(61,28,413) = 100772

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 60/61, 28/28, 406/413

1. What is the HCF of 60,28,406?

The HCF of 60,28,406 is 2

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 60/61, 28/28, 406/413?

Answer: GCF of Numerators as per given numbers 60/61, 28/28, 406/413 is

GCF of Numerators i.e. for 60,28,406 is 2

LCM of denominators i.e. for 61,28,413 is 100772.

Thus, GCF of Fractions is 2/100772.Finally, GCF of Fractions for 60/61, 28/28, 406/413 is 2/100772.