Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 490/219,9000/3564
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 490,9000
Greatest Common Factor of Numerators i.e. GCF of 490,9000 is 10 .
LCM of Denominators means LCM of 219,3564 as per the given fractions.
LCM of 219,3564 is 260172 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 490,9000
2 | 490, 9000 |
5 | 245, 4500 |
49, 900 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Factors of 490
List of positive integer factors of 490 that divides 490 without a remainder.
1,2,5,7,10,14,35,49,70,98,245,490
Factors of 9000
List of positive integer factors of 9000 that divides 9000 without a remainder.
1,2,3,4,5,6,8,9,10,12,15,18,20,24,25,30,36,40,45,50,60,72,75,90,100,120,125,150,180,200,225,250,300,360,375,450,500,600,750,900,1000,1125,1500,1800,2250,3000,4500,9000
Greatest Common Factor
We found the factors 490,9000 . The biggest common factor number is the GCF number.
So the greatest common factor 490,9000 is 10.
Lets's calculate LCM of 219,3564
3 | 219, 3564 |
73, 1188 |
∴ So the LCM of the given numbers is 3 x 73 x 1188 = 260172
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/260172
Therefore, the GCF of Fractions 490/219,9000/3564 is 10/260172
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 219,3564 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,3564) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,3564) x common factors =3 x 1 = 3
LCM(219,3564) = ( 219 × 3564 ) / 3
LCM(219,3564) = 780516 / 3
LCM(219,3564) = 260172
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 490/219, 9000/3564?
Answer: GCF of Numerators as per given numbers 490/219, 9000/3564 is
GCF of Numerators i.e. for 490,9000 is 10
LCM of denominators i.e. for 219,3564 is 260172.
Thus, GCF of Fractions is 10/260172.Finally, GCF of Fractions for 490/219, 9000/3564 is 10/260172.