Use our free GCF of Fractions Calculator tool to compute the GCF of 210/324, 220/984 i.e 10/26568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/324, 220/984.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 210/324,220/984
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 210/324,220/984, numerators are 210,220
Denominators are 324,984
The GCF of 210,220 is 10 .
LCM of 324,984 is 26568.
The greatest common factor of 210/324,220/984 = [GCF of 210,220]/[LCM of 324,984]= 10/26568
Therefore, the GCF of 210/324,220/984 is 10/26568.
To find the highest common factor of 210,220, we have to find the factors of both numbers and list the highest common factor.
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The HCF of 210,220 is 10.
Lets's calculate GCF of 210,220
2 | 210, 220 |
5 | 105, 110 |
21, 22 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Now, list down the factors of 220
:1,2,4,5,10,11,20,22,44,55,110,220
Greatest Common Factor
We found the factors 210,220 . The biggest common factor number is the GCF number.
So the greatest common factor 210,220 is 10.
Lets's calculate LCM of 324,984
2 | 324, 984 |
2 | 162, 492 |
3 | 81, 246 |
27, 82 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 27 x 82 = 26568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/26568
Therefore, the GCF of Fractions 210/324,220/984 is 10/26568
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 324,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,984) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(324,984) x common factors =12 x 1 = 12
LCM(324,984) = ( 324 × 984 ) / 12
LCM(324,984) = 318816 / 12
LCM(324,984) = 26568
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 210,220?
The HCF of 210,220 is 10
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 210/324, 220/984?
Answer: GCF of Numerators as per given numbers 210/324, 220/984 is
GCF of Numerators i.e. for 210,220 is 10
LCM of denominators i.e. for 324,984 is 26568.
Thus, GCF of Fractions is 10/26568.Finally, GCF of Fractions for 210/324, 220/984 is 10/26568.