Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/90,72/98,420/210
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 66,72,420
Greatest Common Factor of Numerators i.e. GCF of 66,72,420 is 6 .
LCM of Denominators means LCM of 90,98,210 as per the given fractions.
LCM of 90,98,210 is 4410 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 66,72,420
2 | 66, 72, 420 |
3 | 33, 36, 210 |
11, 12, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 420
List of positive integer factors of 420 that divides 420 without a remainder.
1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 66,72,420 . The biggest common factor number is the GCF number.
So the greatest common factor 66,72,420 is 6.
Lets's calculate LCM of 90,98,210
2 | 90, 98, 210 |
3 | 45, 49, 105 |
5 | 15, 49, 35 |
7 | 3, 49, 7 |
3, 1, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 3 x 1 x 7 = 4410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4410
Therefore, the GCF of Fractions 66/90,72/98,420/210 is 6/4410
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 90,98,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,98,210) = 2
common factors(in case of two or more numbers have common factors) = 210
GCF(90,98,210) x common factors =2 x 210 = 420
LCM(90,98,210) = ( 90 × 98 × 210 ) / 420
LCM(90,98,210) = 1852200 / 420
LCM(90,98,210) = 4410
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 66/90, 72/98, 420/210?
Answer: GCF of Numerators as per given numbers 66/90, 72/98, 420/210 is
GCF of Numerators i.e. for 66,72,420 is 6
LCM of denominators i.e. for 90,98,210 is 4410.
Thus, GCF of Fractions is 6/4410.Finally, GCF of Fractions for 66/90, 72/98, 420/210 is 6/4410.