Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 165/245,180/392,210/486
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 165,180,210
Greatest Common Factor of Numerators i.e. GCF of 165,180,210 is 15 .
LCM of Denominators means LCM of 245,392,486 as per the given fractions.
LCM of 245,392,486 is 476280 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 165,180,210
3 | 165, 180, 210 |
5 | 55, 60, 70 |
11, 12, 14 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1,3,5,11,15,33,55,165
Factors of 180
List of positive integer factors of 180 that divides 180 without a remainder.
1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Factors of 210
List of positive integer factors of 210 that divides 210 without a remainder.
1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 165,180,210 . The biggest common factor number is the GCF number.
So the greatest common factor 165,180,210 is 15.
Lets's calculate LCM of 245,392,486
2 | 245, 392, 486 |
7 | 245, 196, 243 |
7 | 35, 28, 243 |
5, 4, 243 |
∴ So the LCM of the given numbers is 2 x 7 x 7 x 5 x 4 x 243 = 476280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/476280
Therefore, the GCF of Fractions 165/245,180/392,210/486 is 15/476280
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 245,392,486 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(245,392,486) = 1
common factors(in case of two or more numbers have common factors) = 98
GCF(245,392,486) x common factors =1 x 98 = 98
LCM(245,392,486) = ( 245 × 392 × 486 ) / 98
LCM(245,392,486) = 46675440 / 98
LCM(245,392,486) = 476280
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 165/245, 180/392, 210/486?
Answer: GCF of Numerators as per given numbers 165/245, 180/392, 210/486 is
GCF of Numerators i.e. for 165,180,210 is 15
LCM of denominators i.e. for 245,392,486 is 476280.
Thus, GCF of Fractions is 15/476280.Finally, GCF of Fractions for 165/245, 180/392, 210/486 is 15/476280.