Use our free GCF of Fractions Calculator tool to compute the GCF of 15/84, 360/70, 105/825 i.e 15/23100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/84, 360/70, 105/825.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 15/84,360/70,105/825
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 15/84,360/70,105/825, numerators are 15,360,105
Denominators are 84,70,825
The GCF of 15,360,105 is 15 .
LCM of 84,70,825 is 23100.
The greatest common factor of 15/84,360/70,105/825 = [GCF of 15,360,105]/[LCM of 84,70,825]= 15/23100
Therefore, the GCF of 15/84,360/70,105/825 is 15/23100.
To find the highest common factor of 15,360,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 15 are 1, 3, 5, 15
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 15,360,105 is 15.
Lets's calculate GCF of 15,360,105
3 | 15, 360, 105 |
5 | 5, 120, 35 |
1, 24, 7 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 15,360,105 . The biggest common factor number is the GCF number.
So the greatest common factor 15,360,105 is 15.
Lets's calculate LCM of 84,70,825
2 | 84, 70, 825 |
3 | 42, 35, 825 |
5 | 14, 35, 275 |
7 | 14, 7, 55 |
2, 1, 55 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 2 x 1 x 55 = 23100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/23100
Therefore, the GCF of Fractions 15/84,360/70,105/825 is 15/23100
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 84,70,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,70,825) = 1
common factors(in case of two or more numbers have common factors) = 210
GCF(84,70,825) x common factors =1 x 210 = 210
LCM(84,70,825) = ( 84 × 70 × 825 ) / 210
LCM(84,70,825) = 4851000 / 210
LCM(84,70,825) = 23100
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 15,360,105?
The HCF of 15,360,105 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 15/84, 360/70, 105/825?
Answer: GCF of Numerators as per given numbers 15/84, 360/70, 105/825 is
GCF of Numerators i.e. for 15,360,105 is 15
LCM of denominators i.e. for 84,70,825 is 23100.
Thus, GCF of Fractions is 15/23100.Finally, GCF of Fractions for 15/84, 360/70, 105/825 is 15/23100.