Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 33/20,15/80,84/32,33/749
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 33,15,84,33
Greatest Common Factor of Numerators i.e. GCF of 33,15,84,33 is 3 .
LCM of Denominators means LCM of 20,80,32,749 as per the given fractions.
LCM of 20,80,32,749 is 119840 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 33,15,84,33
3 | 33, 15, 84, 33 |
11, 5, 28, 11 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Greatest Common Factor
We found the factors 33,15,84,33 . The biggest common factor number is the GCF number.
So the greatest common factor 33,15,84,33 is 3.
Lets's calculate LCM of 20,80,32,749
2 | 20, 80, 32, 749 |
2 | 10, 40, 16, 749 |
2 | 5, 20, 8, 749 |
2 | 5, 10, 4, 749 |
5 | 5, 5, 2, 749 |
1, 1, 2, 749 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 1 x 1 x 2 x 749 = 119840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/119840
Therefore, the GCF of Fractions 33/20,15/80,84/32,33/749 is 3/119840
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 20,80,32,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,80,32,749) = 1
common factors(in case of two or more numbers have common factors) = 320
GCF(20,80,32,749) x common factors =1 x 320 = 320
LCM(20,80,32,749) = ( 20 × 80 × 32 × 749 ) / 320
LCM(20,80,32,749) = 38348800 / 320
LCM(20,80,32,749) = 119840
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 33/20, 15/80, 84/32, 33/749?
Answer: GCF of Numerators as per given numbers 33/20, 15/80, 84/32, 33/749 is
GCF of Numerators i.e. for 33,15,84,33 is 3
LCM of denominators i.e. for 20,80,32,749 is 119840.
Thus, GCF of Fractions is 3/119840.Finally, GCF of Fractions for 33/20, 15/80, 84/32, 33/749 is 3/119840.