GCF of 340/684, 135/844, 824/410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 340/684, 135/844, 824/410 i.e 1/29586420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/684, 135/844, 824/410.
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 340/684,135/844,824/410?
Given fractions are 340/684,135/844,824/410
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 340/684,135/844,824/410, numerators are 340,135,824
Denominators are 684,844,410
The GCF of 340,135,824 is 1 .
LCM of 684,844,410 is 29586420.
The greatest common factor of 340/684,135/844,824/410 = [GCF of 340,135,824]/[LCM of 684,844,410]= 1/29586420
Therefore, the GCF of 340/684,135/844,824/410 is 1/29586420.
To find the highest common factor of 340,135,824, we have to find the factors of both numbers and list the highest common factor.
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824
The HCF of 340,135,824 is 1.
Lets's calculate GCF of 340,135,824
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 340,135,824 By Matching Biggest Common Factor Method
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Now, list down the factors of 824
:1,2,4,8,103,206,412,824
Greatest Common Factor
We found the factors 340,135,824 . The biggest common factor number is the GCF number.
So the greatest common factor 340,135,824 is 1.
Lets's calculate LCM of 684,844,410
| 2 | 684, 844, 410 |
| 2 | 342, 422, 205 |
| 171, 211, 205 |
∴ So the LCM of the given numbers is 2 x 2 x 171 x 211 x 205 = 29586420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29586420
Therefore, the GCF of Fractions 340/684,135/844,824/410 is 1/29586420
Least Common Multiple of 684,844,410 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 684,844,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,844,410) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(684,844,410) x common factors =2 x 4 = 8
LCM(684,844,410) = ( 684 × 844 × 410 ) / 8
LCM(684,844,410) = 236691360 / 8
LCM(684,844,410) = 29586420
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 340/684, 135/844, 824/410
1. What is the HCF of 340,135,824?
The HCF of 340,135,824 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 340/684, 135/844, 824/410?
Answer: GCF of Numerators as per given numbers 340/684, 135/844, 824/410 is
GCF of Numerators i.e. for 340,135,824 is 1
LCM of denominators i.e. for 684,844,410 is 29586420.
Thus, GCF of Fractions is 1/29586420.Finally, GCF of Fractions for 340/684, 135/844, 824/410 is 1/29586420.