Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/16,92/48,43/36,36/416
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 31,92,43,36
Greatest Common Factor of Numerators i.e. GCF of 31,92,43,36 is 1 .
LCM of Denominators means LCM of 16,48,36,416 as per the given fractions.
LCM of 16,48,36,416 is 3744 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 31,92,43,36
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 92
List of positive integer factors of 92 that divides 92 without a remainder.
1,2,4,23,46,92
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Greatest Common Factor
We found the factors 31,92,43,36 . The biggest common factor number is the GCF number.
So the greatest common factor 31,92,43,36 is 1.
Lets's calculate LCM of 16,48,36,416
2 | 16, 48, 36, 416 |
2 | 8, 24, 18, 208 |
2 | 4, 12, 9, 104 |
2 | 2, 6, 9, 52 |
3 | 1, 3, 9, 26 |
1, 1, 3, 26 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 1 x 1 x 3 x 26 = 3744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3744
Therefore, the GCF of Fractions 31/16,92/48,43/36,36/416 is 1/3744
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 16,48,36,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,48,36,416) = 4
common factors(in case of two or more numbers have common factors) = 768
GCF(16,48,36,416) x common factors =4 x 768 = 3072
LCM(16,48,36,416) = ( 16 × 48 × 36 × 416 ) / 3072
LCM(16,48,36,416) = 11501568 / 3072
LCM(16,48,36,416) = 3744
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 31/16, 92/48, 43/36, 36/416?
Answer: GCF of Numerators as per given numbers 31/16, 92/48, 43/36, 36/416 is
GCF of Numerators i.e. for 31,92,43,36 is 1
LCM of denominators i.e. for 16,48,36,416 is 3744.
Thus, GCF of Fractions is 1/3744.Finally, GCF of Fractions for 31/16, 92/48, 43/36, 36/416 is 1/3744.