Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 399/58,225/14,168/21
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 399,225,168
Greatest Common Factor of Numerators i.e. GCF of 399,225,168 is 3 .
LCM of Denominators means LCM of 58,14,21 as per the given fractions.
LCM of 58,14,21 is 1218 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 399,225,168
3 | 399, 225, 168 |
133, 75, 56 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 399
List of positive integer factors of 399 that divides 399 without a remainder.
1,3,7,19,21,57,133,399
Factors of 225
List of positive integer factors of 225 that divides 225 without a remainder.
1,3,5,9,15,25,45,75,225
Factors of 168
List of positive integer factors of 168 that divides 168 without a remainder.
1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Greatest Common Factor
We found the factors 399,225,168 . The biggest common factor number is the GCF number.
So the greatest common factor 399,225,168 is 3.
Lets's calculate LCM of 58,14,21
2 | 58, 14, 21 |
7 | 29, 7, 21 |
29, 1, 3 |
∴ So the LCM of the given numbers is 2 x 7 x 29 x 1 x 3 = 1218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1218
Therefore, the GCF of Fractions 399/58,225/14,168/21 is 3/1218
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 58,14,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,14,21) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(58,14,21) x common factors =1 x 14 = 14
LCM(58,14,21) = ( 58 × 14 × 21 ) / 14
LCM(58,14,21) = 17052 / 14
LCM(58,14,21) = 1218
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 399/58, 225/14, 168/21?
Answer: GCF of Numerators as per given numbers 399/58, 225/14, 168/21 is
GCF of Numerators i.e. for 399,225,168 is 3
LCM of denominators i.e. for 58,14,21 is 1218.
Thus, GCF of Fractions is 3/1218.Finally, GCF of Fractions for 399/58, 225/14, 168/21 is 3/1218.