Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/30,14/16,16/60,25/266
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 21,14,16,25
Greatest Common Factor of Numerators i.e. GCF of 21,14,16,25 is 1 .
LCM of Denominators means LCM of 30,16,60,266 as per the given fractions.
LCM of 30,16,60,266 is 31920 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 21,14,16,25
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Greatest Common Factor
We found the factors 21,14,16,25 . The biggest common factor number is the GCF number.
So the greatest common factor 21,14,16,25 is 1.
Lets's calculate LCM of 30,16,60,266
2 | 30, 16, 60, 266 |
2 | 15, 8, 30, 133 |
3 | 15, 4, 15, 133 |
5 | 5, 4, 5, 133 |
1, 4, 1, 133 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 4 x 1 x 133 = 31920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31920
Therefore, the GCF of Fractions 21/30,14/16,16/60,25/266 is 1/31920
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 30,16,60,266 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,16,60,266) = 2
common factors(in case of two or more numbers have common factors) = 120
GCF(30,16,60,266) x common factors =2 x 120 = 240
LCM(30,16,60,266) = ( 30 × 16 × 60 × 266 ) / 240
LCM(30,16,60,266) = 7660800 / 240
LCM(30,16,60,266) = 31920
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 21/30, 14/16, 16/60, 25/266?
Answer: GCF of Numerators as per given numbers 21/30, 14/16, 16/60, 25/266 is
GCF of Numerators i.e. for 21,14,16,25 is 1
LCM of denominators i.e. for 30,16,60,266 is 31920.
Thus, GCF of Fractions is 1/31920.Finally, GCF of Fractions for 21/30, 14/16, 16/60, 25/266 is 1/31920.