Use our free GCF of Fractions Calculator tool to compute the GCF of 319/843, 825/264 i.e 11/74184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/843, 825/264.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 319/843,825/264
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 319/843,825/264, numerators are 319,825
Denominators are 843,264
The GCF of 319,825 is 11 .
LCM of 843,264 is 74184.
The greatest common factor of 319/843,825/264 = [GCF of 319,825]/[LCM of 843,264]= 11/74184
Therefore, the GCF of 319/843,825/264 is 11/74184.
To find the highest common factor of 319,825, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The HCF of 319,825 is 11.
Lets's calculate GCF of 319,825
11 | 319, 825 |
29, 75 |
∴ So the GCF of the given numbers is 11 = 11
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Greatest Common Factor
We found the factors 319,825 . The biggest common factor number is the GCF number.
So the greatest common factor 319,825 is 11.
Lets's calculate LCM of 843,264
3 | 843, 264 |
281, 88 |
∴ So the LCM of the given numbers is 3 x 281 x 88 = 74184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/74184
Therefore, the GCF of Fractions 319/843,825/264 is 11/74184
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 843,264 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(843,264) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(843,264) x common factors =3 x 1 = 3
LCM(843,264) = ( 843 × 264 ) / 3
LCM(843,264) = 222552 / 3
LCM(843,264) = 74184
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 319,825?
The HCF of 319,825 is 11
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 319/843, 825/264?
Answer: GCF of Numerators as per given numbers 319/843, 825/264 is
GCF of Numerators i.e. for 319,825 is 11
LCM of denominators i.e. for 843,264 is 74184.
Thus, GCF of Fractions is 11/74184.Finally, GCF of Fractions for 319/843, 825/264 is 11/74184.