GCF of 81/816, 600/880, 414/900
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 81/816, 600/880, 414/900 i.e 3/673200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 81/816, 600/880, 414/900.
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 81/816,600/880,414/900?
Given fractions are 81/816,600/880,414/900
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 81/816,600/880,414/900, numerators are 81,600,414
Denominators are 816,880,900
The GCF of 81,600,414 is 3 .
LCM of 816,880,900 is 673200.
The greatest common factor of 81/816,600/880,414/900 = [GCF of 81,600,414]/[LCM of 816,880,900]= 3/673200
Therefore, the GCF of 81/816,600/880,414/900 is 3/673200.
To find the highest common factor of 81,600,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 81 are 1, 3, 9, 27, 81
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 81,600,414 is 3.
Lets's calculate GCF of 81,600,414
| 3 | 81, 600, 414 |
| 27, 200, 138 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 81,600,414 By Matching Biggest Common Factor Method
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 81,600,414 . The biggest common factor number is the GCF number.
So the greatest common factor 81,600,414 is 3.
Lets's calculate LCM of 816,880,900
| 2 | 816, 880, 900 |
| 2 | 408, 440, 450 |
| 2 | 204, 220, 225 |
| 2 | 102, 110, 225 |
| 3 | 51, 55, 225 |
| 5 | 17, 55, 75 |
| 17, 11, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 5 x 17 x 11 x 15 = 673200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/673200
Therefore, the GCF of Fractions 81/816,600/880,414/900 is 3/673200
Least Common Multiple of 816,880,900 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 816,880,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(816,880,900) = 4
common factors(in case of two or more numbers have common factors) = 240
GCF(816,880,900) x common factors =4 x 240 = 960
LCM(816,880,900) = ( 816 × 880 × 900 ) / 960
LCM(816,880,900) = 646272000 / 960
LCM(816,880,900) = 673200
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 81/816, 600/880, 414/900
1. What is the HCF of 81,600,414?
The HCF of 81,600,414 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 81/816, 600/880, 414/900?
Answer: GCF of Numerators as per given numbers 81/816, 600/880, 414/900 is
GCF of Numerators i.e. for 81,600,414 is 3
LCM of denominators i.e. for 816,880,900 is 673200.
Thus, GCF of Fractions is 3/673200.Finally, GCF of Fractions for 81/816, 600/880, 414/900 is 3/673200.