Use our free GCF of Fractions Calculator tool to compute the GCF of 180/970, 612/825 i.e 36/160050 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/970, 612/825.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 180/970,612/825
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 180/970,612/825, numerators are 180,612
Denominators are 970,825
The GCF of 180,612 is 36 .
LCM of 970,825 is 160050.
The greatest common factor of 180/970,612/825 = [GCF of 180,612]/[LCM of 970,825]= 36/160050
Therefore, the GCF of 180/970,612/825 is 36/160050.
To find the highest common factor of 180,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 180,612 is 36.
Lets's calculate GCF of 180,612
2 | 180, 612 |
2 | 90, 306 |
3 | 45, 153 |
3 | 15, 51 |
5, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 180,612 . The biggest common factor number is the GCF number.
So the greatest common factor 180,612 is 36.
Lets's calculate LCM of 970,825
5 | 970, 825 |
194, 165 |
∴ So the LCM of the given numbers is 5 x 194 x 165 = 160050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/160050
Therefore, the GCF of Fractions 180/970,612/825 is 36/160050
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 970,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(970,825) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(970,825) x common factors =5 x 1 = 5
LCM(970,825) = ( 970 × 825 ) / 5
LCM(970,825) = 800250 / 5
LCM(970,825) = 160050
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 180,612?
The HCF of 180,612 is 36
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 180/970, 612/825?
Answer: GCF of Numerators as per given numbers 180/970, 612/825 is
GCF of Numerators i.e. for 180,612 is 36
LCM of denominators i.e. for 970,825 is 160050.
Thus, GCF of Fractions is 36/160050.Finally, GCF of Fractions for 180/970, 612/825 is 36/160050.