How to Find GCF of 13/362, 30/357, 289/606?

GCF of 13/362, 30/357, 289/606

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 13/362, 30/357, 289/606 i.e 1/13052634 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/362, 30/357, 289/606.

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 13/362,30/357,289/606?

Given fractions are 13/362,30/357,289/606

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 13/362,30/357,289/606, numerators are 13,30,289

Denominators are 362,357,606

The GCF of 13,30,289 is 1 .

LCM of 362,357,606 is 13052634.

The greatest common factor of 13/362,30/357,289/606 = [GCF of 13,30,289]/[LCM of 362,357,606]= 1/13052634

Therefore, the GCF of 13/362,30/357,289/606 is 1/13052634.

Greatest Common Factor of 13,30,289

To find the highest common factor of 13,30,289, 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 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 289 are 1, 17, 289

The HCF of 13,30,289 is 1.

Lets's calculate GCF of 13,30,289

Greatest Common Factor (GCF) of 13,30,289 By Common Division

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

Greatest Common Factor of 13,30,289 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 289

1,17,289

Greatest Common Factor

We found the factors 13,30,289 . The biggest common factor number is the GCF number.
So the greatest common factor 13,30,289 is 1.

Lets's calculate LCM of 362,357,606

Lowest Common Multiple of 362,357,606 using Common Division

2	362, 357, 606
3	181, 357, 303
	181, 119, 101

∴ So the LCM of the given numbers is 2 x 3 x 181 x 119 x 101 = 13052634

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13052634

Therefore, the GCF of Fractions 13/362,30/357,289/606 is 1/13052634

Least Common Multiple of 362,357,606 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 362,357,606 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(362,357,606) = 1

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

GCF(362,357,606) x common factors =1 x 6 = 6

LCM(362,357,606) = ( 362 × 357 × 606 ) / 6

LCM(362,357,606) = 78315804 / 6

LCM(362,357,606) = 13052634

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FAQs on GCF of Fractions of 13/362, 30/357, 289/606

1. What is the HCF of 13,30,289?

The HCF of 13,30,289 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 13/362, 30/357, 289/606?

Answer: GCF of Numerators as per given numbers 13/362, 30/357, 289/606 is

GCF of Numerators i.e. for 13,30,289 is 1

LCM of denominators i.e. for 362,357,606 is 13052634.

Thus, GCF of Fractions is 1/13052634.Finally, GCF of Fractions for 13/362, 30/357, 289/606 is 1/13052634.