Use our free GCF of Fractions Calculator tool to compute the GCF of 459/619, 324/753 i.e 27/466107 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/619, 324/753.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 459/619,324/753
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 459/619,324/753, numerators are 459,324
Denominators are 619,753
The GCF of 459,324 is 27 .
LCM of 619,753 is 466107.
The greatest common factor of 459/619,324/753 = [GCF of 459,324]/[LCM of 619,753]= 27/466107
Therefore, the GCF of 459/619,324/753 is 27/466107.
To find the highest common factor of 459,324, we have to find the factors of both numbers and list the highest common factor.
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The HCF of 459,324 is 27.
Lets's calculate GCF of 459,324
3 | 459, 324 |
3 | 153, 108 |
3 | 51, 36 |
17, 12 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Greatest Common Factor
We found the factors 459,324 . The biggest common factor number is the GCF number.
So the greatest common factor 459,324 is 27.
Lets's calculate LCM of 619,753
Given numbers has no common factors except 1. So, there LCM is their product i.e 466107
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/466107
Therefore, the GCF of Fractions 459/619,324/753 is 27/466107
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 619,753 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(619,753) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(619,753) x common factors =1 x 1 = 1
LCM(619,753) = ( 619 × 753 ) / 1
LCM(619,753) = 466107 / 1
LCM(619,753) = 466107
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 459,324?
The HCF of 459,324 is 27
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 459/619, 324/753?
Answer: GCF of Numerators as per given numbers 459/619, 324/753 is
GCF of Numerators i.e. for 459,324 is 27
LCM of denominators i.e. for 619,753 is 466107.
Thus, GCF of Fractions is 27/466107.Finally, GCF of Fractions for 459/619, 324/753 is 27/466107.