Use our free GCF of Fractions Calculator tool to compute the GCF of 432/878, 612/798 i.e 36/350322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/878, 612/798.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 432/878,612/798
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 432/878,612/798, numerators are 432,612
Denominators are 878,798
The GCF of 432,612 is 36 .
LCM of 878,798 is 350322.
The greatest common factor of 432/878,612/798 = [GCF of 432,612]/[LCM of 878,798]= 36/350322
Therefore, the GCF of 432/878,612/798 is 36/350322.
To find the highest common factor of 432,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
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 432,612 is 36.
Lets's calculate GCF of 432,612
2 | 432, 612 |
2 | 216, 306 |
3 | 108, 153 |
3 | 36, 51 |
12, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
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 432,612 . The biggest common factor number is the GCF number.
So the greatest common factor 432,612 is 36.
Lets's calculate LCM of 878,798
2 | 878, 798 |
439, 399 |
∴ So the LCM of the given numbers is 2 x 439 x 399 = 350322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/350322
Therefore, the GCF of Fractions 432/878,612/798 is 36/350322
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 878,798 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(878,798) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(878,798) x common factors =2 x 1 = 2
LCM(878,798) = ( 878 × 798 ) / 2
LCM(878,798) = 700644 / 2
LCM(878,798) = 350322
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 432,612?
The HCF of 432,612 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 432/878, 612/798?
Answer: GCF of Numerators as per given numbers 432/878, 612/798 is
GCF of Numerators i.e. for 432,612 is 36
LCM of denominators i.e. for 878,798 is 350322.
Thus, GCF of Fractions is 36/350322.Finally, GCF of Fractions for 432/878, 612/798 is 36/350322.