How to Find GCF of 66/814, 300/199, 223/333?

GCF of 66/814, 300/199, 223/333

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 66/814, 300/199, 223/333 i.e 1/1457874 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/814, 300/199, 223/333.

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 66/814,300/199,223/333?

Given fractions are 66/814,300/199,223/333

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 66/814,300/199,223/333, numerators are 66,300,223

Denominators are 814,199,333

The GCF of 66,300,223 is 1 .

LCM of 814,199,333 is 1457874.

The greatest common factor of 66/814,300/199,223/333 = [GCF of 66,300,223]/[LCM of 814,199,333]= 1/1457874

Therefore, the GCF of 66/814,300/199,223/333 is 1/1457874.

Greatest Common Factor of 66,300,223

To find the highest common factor of 66,300,223, 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 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The factors of 223 are 1, 223

The HCF of 66,300,223 is 1.

Lets's calculate GCF of 66,300,223

Greatest Common Factor (GCF) of 66,300,223 By Common Division

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

Greatest Common Factor of 66,300,223 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 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Now, list down the factors of 223

1,223

Greatest Common Factor

We found the factors 66,300,223 . The biggest common factor number is the GCF number.
So the greatest common factor 66,300,223 is 1.

Lets's calculate LCM of 814,199,333

Lowest Common Multiple of 814,199,333 using Common Division

37	814, 199, 333
	22, 199, 9

∴ So the LCM of the given numbers is 37 x 22 x 199 x 9 = 1457874

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1457874

Therefore, the GCF of Fractions 66/814,300/199,223/333 is 1/1457874

Least Common Multiple of 814,199,333 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 814,199,333 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(814,199,333) = 1

common factors(in case of two or more numbers have common factors) = 37

GCF(814,199,333) x common factors =1 x 37 = 37

LCM(814,199,333) = ( 814 × 199 × 333 ) / 37

LCM(814,199,333) = 53941338 / 37

LCM(814,199,333) = 1457874

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 66/814, 300/199, 223/333

1. What is the HCF of 66,300,223?

The HCF of 66,300,223 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 66/814, 300/199, 223/333?

Answer: GCF of Numerators as per given numbers 66/814, 300/199, 223/333 is

GCF of Numerators i.e. for 66,300,223 is 1

LCM of denominators i.e. for 814,199,333 is 1457874.

Thus, GCF of Fractions is 1/1457874.Finally, GCF of Fractions for 66/814, 300/199, 223/333 is 1/1457874.