Use our free GCF of Fractions Calculator tool to compute the GCF of 2160/680, 8205/7322 i.e 15/2489480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2160/680, 8205/7322.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2160/680,8205/7322
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 2160/680,8205/7322, numerators are 2160,8205
Denominators are 680,7322
The GCF of 2160,8205 is 15 .
LCM of 680,7322 is 2489480.
The greatest common factor of 2160/680,8205/7322 = [GCF of 2160,8205]/[LCM of 680,7322]= 15/2489480
Therefore, the GCF of 2160/680,8205/7322 is 15/2489480.
To find the highest common factor of 2160,8205, we have to find the factors of both numbers and list the highest common factor.
The factors of 2160 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160
The factors of 8205 are 1, 3, 5, 15, 547, 1641, 2735, 8205
The HCF of 2160,8205 is 15.
Lets's calculate GCF of 2160,8205
3 | 2160, 8205 |
5 | 720, 2735 |
144, 547 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Now, list down the factors of 2160
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,36,40,45,48,54,60,72,80,90,108,120,135,144,180,216,240,270,360,432,540,720,1080,2160
Now, list down the factors of 8205
:1,3,5,15,547,1641,2735,8205
Greatest Common Factor
We found the factors 2160,8205 . The biggest common factor number is the GCF number.
So the greatest common factor 2160,8205 is 15.
Lets's calculate LCM of 680,7322
2 | 680, 7322 |
340, 3661 |
∴ So the LCM of the given numbers is 2 x 340 x 3661 = 2489480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/2489480
Therefore, the GCF of Fractions 2160/680,8205/7322 is 15/2489480
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 680,7322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,7322) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(680,7322) x common factors =2 x 1 = 2
LCM(680,7322) = ( 680 × 7322 ) / 2
LCM(680,7322) = 4978960 / 2
LCM(680,7322) = 2489480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2160,8205?
The HCF of 2160,8205 is 15
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 2160/680, 8205/7322?
Answer: GCF of Numerators as per given numbers 2160/680, 8205/7322 is
GCF of Numerators i.e. for 2160,8205 is 15
LCM of denominators i.e. for 680,7322 is 2489480.
Thus, GCF of Fractions is 15/2489480.Finally, GCF of Fractions for 2160/680, 8205/7322 is 15/2489480.