Use our free GCF of Fractions Calculator tool to compute the GCF of 489/417, 630/578 i.e 3/241026 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/417, 630/578.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 489/417,630/578
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 489/417,630/578, numerators are 489,630
Denominators are 417,578
The GCF of 489,630 is 3 .
LCM of 417,578 is 241026.
The greatest common factor of 489/417,630/578 = [GCF of 489,630]/[LCM of 417,578]= 3/241026
Therefore, the GCF of 489/417,630/578 is 3/241026.
To find the highest common factor of 489,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 489 are 1, 3, 163, 489
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The HCF of 489,630 is 3.
Lets's calculate GCF of 489,630
3 | 489, 630 |
163, 210 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Greatest Common Factor
We found the factors 489,630 . The biggest common factor number is the GCF number.
So the greatest common factor 489,630 is 3.
Lets's calculate LCM of 417,578
Given numbers has no common factors except 1. So, there LCM is their product i.e 241026
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/241026
Therefore, the GCF of Fractions 489/417,630/578 is 3/241026
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 417,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(417,578) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(417,578) x common factors =1 x 1 = 1
LCM(417,578) = ( 417 × 578 ) / 1
LCM(417,578) = 241026 / 1
LCM(417,578) = 241026
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 489,630?
The HCF of 489,630 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 489/417, 630/578?
Answer: GCF of Numerators as per given numbers 489/417, 630/578 is
GCF of Numerators i.e. for 489,630 is 3
LCM of denominators i.e. for 417,578 is 241026.
Thus, GCF of Fractions is 3/241026.Finally, GCF of Fractions for 489/417, 630/578 is 3/241026.