Use our free GCF of Fractions Calculator tool to compute the GCF of 450/272, 612/160 i.e 18/2720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/272, 612/160.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 450/272,612/160
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 450/272,612/160, numerators are 450,612
Denominators are 272,160
The GCF of 450,612 is 18 .
LCM of 272,160 is 2720.
The greatest common factor of 450/272,612/160 = [GCF of 450,612]/[LCM of 272,160]= 18/2720
Therefore, the GCF of 450/272,612/160 is 18/2720.
To find the highest common factor of 450,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
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 450,612 is 18.
Lets's calculate GCF of 450,612
2 | 450, 612 |
3 | 225, 306 |
3 | 75, 102 |
25, 34 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
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 450,612 . The biggest common factor number is the GCF number.
So the greatest common factor 450,612 is 18.
Lets's calculate LCM of 272,160
2 | 272, 160 |
2 | 136, 80 |
2 | 68, 40 |
2 | 34, 20 |
17, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 17 x 10 = 2720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/2720
Therefore, the GCF of Fractions 450/272,612/160 is 18/2720
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 272,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(272,160) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(272,160) x common factors =16 x 1 = 16
LCM(272,160) = ( 272 × 160 ) / 16
LCM(272,160) = 43520 / 16
LCM(272,160) = 2720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 450,612?
The HCF of 450,612 is 18
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 450/272, 612/160?
Answer: GCF of Numerators as per given numbers 450/272, 612/160 is
GCF of Numerators i.e. for 450,612 is 18
LCM of denominators i.e. for 272,160 is 2720.
Thus, GCF of Fractions is 18/2720.Finally, GCF of Fractions for 450/272, 612/160 is 18/2720.