Use our free GCF of Fractions Calculator tool to compute the GCF of 576/772, 180/624 i.e 36/120432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 576/772, 180/624.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 576/772,180/624
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 576/772,180/624, numerators are 576,180
Denominators are 772,624
The GCF of 576,180 is 36 .
LCM of 772,624 is 120432.
The greatest common factor of 576/772,180/624 = [GCF of 576,180]/[LCM of 772,624]= 36/120432
Therefore, the GCF of 576/772,180/624 is 36/120432.
To find the highest common factor of 576,180, we have to find the factors of both numbers and list the highest common factor.
The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 576,180 is 36.
Lets's calculate GCF of 576,180
2 | 576, 180 |
2 | 288, 90 |
3 | 144, 45 |
3 | 48, 15 |
16, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
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
Greatest Common Factor
We found the factors 576,180 . The biggest common factor number is the GCF number.
So the greatest common factor 576,180 is 36.
Lets's calculate LCM of 772,624
2 | 772, 624 |
2 | 386, 312 |
193, 156 |
∴ So the LCM of the given numbers is 2 x 2 x 193 x 156 = 120432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/120432
Therefore, the GCF of Fractions 576/772,180/624 is 36/120432
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 772,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(772,624) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(772,624) x common factors =4 x 1 = 4
LCM(772,624) = ( 772 × 624 ) / 4
LCM(772,624) = 481728 / 4
LCM(772,624) = 120432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 576,180?
The HCF of 576,180 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 576/772, 180/624?
Answer: GCF of Numerators as per given numbers 576/772, 180/624 is
GCF of Numerators i.e. for 576,180 is 36
LCM of denominators i.e. for 772,624 is 120432.
Thus, GCF of Fractions is 36/120432.Finally, GCF of Fractions for 576/772, 180/624 is 36/120432.