Use our free GCF of Fractions Calculator tool to compute the GCF of 417/678, 141/648 i.e 3/73224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/678, 141/648.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 417/678,141/648
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 417/678,141/648, numerators are 417,141
Denominators are 678,648
The GCF of 417,141 is 3 .
LCM of 678,648 is 73224.
The greatest common factor of 417/678,141/648 = [GCF of 417,141]/[LCM of 678,648]= 3/73224
Therefore, the GCF of 417/678,141/648 is 3/73224.
To find the highest common factor of 417,141, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 141 are 1, 3, 47, 141
The HCF of 417,141 is 3.
Lets's calculate GCF of 417,141
3 | 417, 141 |
139, 47 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 141
:1,3,47,141
Greatest Common Factor
We found the factors 417,141 . The biggest common factor number is the GCF number.
So the greatest common factor 417,141 is 3.
Lets's calculate LCM of 678,648
2 | 678, 648 |
3 | 339, 324 |
113, 108 |
∴ So the LCM of the given numbers is 2 x 3 x 113 x 108 = 73224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/73224
Therefore, the GCF of Fractions 417/678,141/648 is 3/73224
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 678,648 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,648) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(678,648) x common factors =6 x 1 = 6
LCM(678,648) = ( 678 × 648 ) / 6
LCM(678,648) = 439344 / 6
LCM(678,648) = 73224
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 417,141?
The HCF of 417,141 is 3
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 417/678, 141/648?
Answer: GCF of Numerators as per given numbers 417/678, 141/648 is
GCF of Numerators i.e. for 417,141 is 3
LCM of denominators i.e. for 678,648 is 73224.
Thus, GCF of Fractions is 3/73224.Finally, GCF of Fractions for 417/678, 141/648 is 3/73224.