Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 33/40,14/46,23/92,42/30
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 33,14,23,42
Greatest Common Factor of Numerators i.e. GCF of 33,14,23,42 is 1 .
LCM of Denominators means LCM of 40,46,92,30 as per the given fractions.
LCM of 40,46,92,30 is 2760 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 33,14,23,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 33,14,23,42 . The biggest common factor number is the GCF number.
So the greatest common factor 33,14,23,42 is 1.
Lets's calculate LCM of 40,46,92,30
2 | 40, 46, 92, 30 |
2 | 20, 23, 46, 15 |
5 | 10, 23, 23, 15 |
23 | 2, 23, 23, 3 |
2, 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 23 x 2 x 1 x 1 x 3 = 2760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2760
Therefore, the GCF of Fractions 33/40,14/46,23/92,42/30 is 1/2760
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 40,46,92,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,46,92,30) = 2
common factors(in case of two or more numbers have common factors) = 920
GCF(40,46,92,30) x common factors =2 x 920 = 1840
LCM(40,46,92,30) = ( 40 × 46 × 92 × 30 ) / 1840
LCM(40,46,92,30) = 5078400 / 1840
LCM(40,46,92,30) = 2760
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 33/40, 14/46, 23/92, 42/30?
Answer: GCF of Numerators as per given numbers 33/40, 14/46, 23/92, 42/30 is
GCF of Numerators i.e. for 33,14,23,42 is 1
LCM of denominators i.e. for 40,46,92,30 is 2760.
Thus, GCF of Fractions is 1/2760.Finally, GCF of Fractions for 33/40, 14/46, 23/92, 42/30 is 1/2760.