How to Find GCF of 66/320, 30/744, 417/361?

GCF of 66/320, 30/744, 417/361

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 66/320, 30/744, 417/361 i.e 3/10743360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/320, 30/744, 417/361.

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 66/320,30/744,417/361?

Given fractions are 66/320,30/744,417/361

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 66/320,30/744,417/361, numerators are 66,30,417

Denominators are 320,744,361

The GCF of 66,30,417 is 3 .

LCM of 320,744,361 is 10743360.

The greatest common factor of 66/320,30/744,417/361 = [GCF of 66,30,417]/[LCM of 320,744,361]= 3/10743360

Therefore, the GCF of 66/320,30/744,417/361 is 3/10743360.

Greatest Common Factor of 66,30,417

To find the highest common factor of 66,30,417, we have to find the factors of both numbers and list the highest common factor.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 417 are 1, 3, 139, 417

The HCF of 66,30,417 is 3.

Lets's calculate GCF of 66,30,417

Greatest Common Factor (GCF) of 66,30,417 By Common Division

3	66, 30, 417
	22, 10, 139

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 66,30,417 By Matching Biggest Common Factor Method

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 30

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

Now, list down the factors of 417

1,3,139,417

Greatest Common Factor

We found the factors 66,30,417 . The biggest common factor number is the GCF number.
So the greatest common factor 66,30,417 is 3.

Lets's calculate LCM of 320,744,361

Lowest Common Multiple of 320,744,361 using Common Division

2	320, 744, 361
2	160, 372, 361
2	80, 186, 361
	40, 93, 361

∴ So the LCM of the given numbers is 2 x 2 x 2 x 40 x 93 x 361 = 10743360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/10743360

Therefore, the GCF of Fractions 66/320,30/744,417/361 is 3/10743360

Least Common Multiple of 320,744,361 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 320,744,361 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,744,361) = 1

common factors(in case of two or more numbers have common factors) = 8

GCF(320,744,361) x common factors =1 x 8 = 8

LCM(320,744,361) = ( 320 × 744 × 361 ) / 8

LCM(320,744,361) = 85946880 / 8

LCM(320,744,361) = 10743360

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 66/320, 30/744, 417/361

1. What is the HCF of 66,30,417?

The HCF of 66,30,417 is 3

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 66/320, 30/744, 417/361?

Answer: GCF of Numerators as per given numbers 66/320, 30/744, 417/361 is

GCF of Numerators i.e. for 66,30,417 is 3

LCM of denominators i.e. for 320,744,361 is 10743360.

Thus, GCF of Fractions is 3/10743360.Finally, GCF of Fractions for 66/320, 30/744, 417/361 is 3/10743360.