How to Find GCF of 65/38, 39/10, 442/300?

GCF of 65/38, 39/10, 442/300

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 65/38, 39/10, 442/300 i.e 13/5700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/38, 39/10, 442/300.

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 65/38,39/10,442/300?

Given fractions are 65/38,39/10,442/300

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 65/38,39/10,442/300, numerators are 65,39,442

Denominators are 38,10,300

The GCF of 65,39,442 is 13 .

LCM of 38,10,300 is 5700.

The greatest common factor of 65/38,39/10,442/300 = [GCF of 65,39,442]/[LCM of 38,10,300]= 13/5700

Therefore, the GCF of 65/38,39/10,442/300 is 13/5700.

Greatest Common Factor of 65,39,442

To find the highest common factor of 65,39,442, we have to find the factors of both numbers and list the highest common factor.

The factors of 65 are 1, 5, 13, 65

The factors of 39 are 1, 3, 13, 39

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

The HCF of 65,39,442 is 13.

Lets's calculate GCF of 65,39,442

Greatest Common Factor (GCF) of 65,39,442 By Common Division

13	65, 39, 442
	5, 3, 34

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 65,39,442 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 39

1,3,13,39

Now, list down the factors of 442

1,2,13,17,26,34,221,442

Greatest Common Factor

We found the factors 65,39,442 . The biggest common factor number is the GCF number.
So the greatest common factor 65,39,442 is 13.

Lets's calculate LCM of 38,10,300

Lowest Common Multiple of 38,10,300 using Common Division

2	38, 10, 300
5	19, 5, 150
	19, 1, 30

∴ So the LCM of the given numbers is 2 x 5 x 19 x 1 x 30 = 5700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/5700

Therefore, the GCF of Fractions 65/38,39/10,442/300 is 13/5700

Least Common Multiple of 38,10,300 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 38,10,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,10,300) = 2

common factors(in case of two or more numbers have common factors) = 10

GCF(38,10,300) x common factors =2 x 10 = 20

LCM(38,10,300) = ( 38 × 10 × 300 ) / 20

LCM(38,10,300) = 114000 / 20

LCM(38,10,300) = 5700

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 65/38, 39/10, 442/300

1. What is the HCF of 65,39,442?

The HCF of 65,39,442 is 13

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 65/38, 39/10, 442/300?

Answer: GCF of Numerators as per given numbers 65/38, 39/10, 442/300 is

GCF of Numerators i.e. for 65,39,442 is 13

LCM of denominators i.e. for 38,10,300 is 5700.

Thus, GCF of Fractions is 13/5700.Finally, GCF of Fractions for 65/38, 39/10, 442/300 is 13/5700.