How to Find GCF of 13/32, 37/99, 159/506?

GCF of 13/32, 37/99, 159/506

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 13/32, 37/99, 159/506 i.e 1/72864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/32, 37/99, 159/506.

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 13/32,37/99,159/506?

Given fractions are 13/32,37/99,159/506

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 13/32,37/99,159/506, numerators are 13,37,159

Denominators are 32,99,506

The GCF of 13,37,159 is 1 .

LCM of 32,99,506 is 72864.

The greatest common factor of 13/32,37/99,159/506 = [GCF of 13,37,159]/[LCM of 32,99,506]= 1/72864

Therefore, the GCF of 13/32,37/99,159/506 is 1/72864.

Greatest Common Factor of 13,37,159

To find the highest common factor of 13,37,159, 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 37 are 1, 37

The factors of 159 are 1, 3, 53, 159

The HCF of 13,37,159 is 1.

Lets's calculate GCF of 13,37,159

Greatest Common Factor (GCF) of 13,37,159 By Common Division

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

Greatest Common Factor of 13,37,159 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 37

1,37

Now, list down the factors of 159

1,3,53,159

Greatest Common Factor

We found the factors 13,37,159 . The biggest common factor number is the GCF number.
So the greatest common factor 13,37,159 is 1.

Lets's calculate LCM of 32,99,506

Lowest Common Multiple of 32,99,506 using Common Division

2	32, 99, 506
11	16, 99, 253
	16, 9, 23

∴ So the LCM of the given numbers is 2 x 11 x 16 x 9 x 23 = 72864

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72864

Therefore, the GCF of Fractions 13/32,37/99,159/506 is 1/72864

Least Common Multiple of 32,99,506 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 32,99,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,99,506) = 1

common factors(in case of two or more numbers have common factors) = 22

GCF(32,99,506) x common factors =1 x 22 = 22

LCM(32,99,506) = ( 32 × 99 × 506 ) / 22

LCM(32,99,506) = 1603008 / 22

LCM(32,99,506) = 72864

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FAQs on GCF of Fractions of 13/32, 37/99, 159/506

1. What is the HCF of 13,37,159?

The HCF of 13,37,159 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 13/32, 37/99, 159/506?

Answer: GCF of Numerators as per given numbers 13/32, 37/99, 159/506 is

GCF of Numerators i.e. for 13,37,159 is 1

LCM of denominators i.e. for 32,99,506 is 72864.

Thus, GCF of Fractions is 1/72864.Finally, GCF of Fractions for 13/32, 37/99, 159/506 is 1/72864.