Use our free GCF of Fractions Calculator tool to compute the GCF of 978/510, 810/423 i.e 6/71910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 978/510, 810/423.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 978/510,810/423
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 978/510,810/423, numerators are 978,810
Denominators are 510,423
The GCF of 978,810 is 6 .
LCM of 510,423 is 71910.
The greatest common factor of 978/510,810/423 = [GCF of 978,810]/[LCM of 510,423]= 6/71910
Therefore, the GCF of 978/510,810/423 is 6/71910.
To find the highest common factor of 978,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 978,810 is 6.
Lets's calculate GCF of 978,810
2 | 978, 810 |
3 | 489, 405 |
163, 135 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 978,810 . The biggest common factor number is the GCF number.
So the greatest common factor 978,810 is 6.
Lets's calculate LCM of 510,423
3 | 510, 423 |
170, 141 |
∴ So the LCM of the given numbers is 3 x 170 x 141 = 71910
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/71910
Therefore, the GCF of Fractions 978/510,810/423 is 6/71910
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 510,423 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(510,423) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(510,423) x common factors =3 x 1 = 3
LCM(510,423) = ( 510 × 423 ) / 3
LCM(510,423) = 215730 / 3
LCM(510,423) = 71910
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 978,810?
The HCF of 978,810 is 6
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 978/510, 810/423?
Answer: GCF of Numerators as per given numbers 978/510, 810/423 is
GCF of Numerators i.e. for 978,810 is 6
LCM of denominators i.e. for 510,423 is 71910.
Thus, GCF of Fractions is 6/71910.Finally, GCF of Fractions for 978/510, 810/423 is 6/71910.