GCF of 66/13, 177/72, 654/229
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 66/13, 177/72, 654/229 i.e 3/214344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/13, 177/72, 654/229.
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 66/13,177/72,654/229?
Given fractions are 66/13,177/72,654/229
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 66/13,177/72,654/229, numerators are 66,177,654
Denominators are 13,72,229
The GCF of 66,177,654 is 3 .
LCM of 13,72,229 is 214344.
The greatest common factor of 66/13,177/72,654/229 = [GCF of 66,177,654]/[LCM of 13,72,229]= 3/214344
Therefore, the GCF of 66/13,177/72,654/229 is 3/214344.
To find the highest common factor of 66,177,654, 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 177 are 1, 3, 59, 177
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 66,177,654 is 3.
Lets's calculate GCF of 66,177,654
| 3 | 66, 177, 654 |
| 22, 59, 218 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 66,177,654 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 177
:1,3,59,177
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 66,177,654 . The biggest common factor number is the GCF number.
So the greatest common factor 66,177,654 is 3.
Lets's calculate LCM of 13,72,229
Given numbers has no common factors except 1. So, there LCM is their product i.e 214344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/214344
Therefore, the GCF of Fractions 66/13,177/72,654/229 is 3/214344
Least Common Multiple of 13,72,229 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 13,72,229 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,72,229) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,72,229) x common factors =1 x 1 = 1
LCM(13,72,229) = ( 13 × 72 × 229 ) / 1
LCM(13,72,229) = 214344 / 1
LCM(13,72,229) = 214344
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 66/13, 177/72, 654/229
1. What is the HCF of 66,177,654?
The HCF of 66,177,654 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 66/13, 177/72, 654/229?
Answer: GCF of Numerators as per given numbers 66/13, 177/72, 654/229 is
GCF of Numerators i.e. for 66,177,654 is 3
LCM of denominators i.e. for 13,72,229 is 214344.
Thus, GCF of Fractions is 3/214344.Finally, GCF of Fractions for 66/13, 177/72, 654/229 is 3/214344.