Use our free GCF of Fractions Calculator tool to compute the GCF of 324/304, 432/692 i.e 108/52592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/304, 432/692.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 324/304,432/692
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 324/304,432/692, numerators are 324,432
Denominators are 304,692
The GCF of 324,432 is 108 .
LCM of 304,692 is 52592.
The greatest common factor of 324/304,432/692 = [GCF of 324,432]/[LCM of 304,692]= 108/52592
Therefore, the GCF of 324/304,432/692 is 108/52592.
To find the highest common factor of 324,432, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
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 HCF of 324,432 is 108.
Lets's calculate GCF of 324,432
2 | 324, 432 |
2 | 162, 216 |
3 | 81, 108 |
3 | 27, 36 |
3 | 9, 12 |
3, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 x 3 = 108
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
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
Greatest Common Factor
We found the factors 324,432 . The biggest common factor number is the GCF number.
So the greatest common factor 324,432 is 108.
Lets's calculate LCM of 304,692
2 | 304, 692 |
2 | 152, 346 |
76, 173 |
∴ So the LCM of the given numbers is 2 x 2 x 76 x 173 = 52592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 108/52592
Therefore, the GCF of Fractions 324/304,432/692 is 108/52592
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 304,692 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,692) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(304,692) x common factors =4 x 1 = 4
LCM(304,692) = ( 304 × 692 ) / 4
LCM(304,692) = 210368 / 4
LCM(304,692) = 52592
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 324,432?
The HCF of 324,432 is 108
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 324/304, 432/692?
Answer: GCF of Numerators as per given numbers 324/304, 432/692 is
GCF of Numerators i.e. for 324,432 is 108
LCM of denominators i.e. for 304,692 is 52592.
Thus, GCF of Fractions is 108/52592.Finally, GCF of Fractions for 324/304, 432/692 is 108/52592.