Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/39,46/31,69/12,57/62
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 54,46,69,57
Greatest Common Factor of Numerators i.e. GCF of 54,46,69,57 is 1 .
LCM of Denominators means LCM of 39,31,12,62 as per the given fractions.
LCM of 39,31,12,62 is 4836 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,46,69,57
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Greatest Common Factor
We found the factors 54,46,69,57 . The biggest common factor number is the GCF number.
So the greatest common factor 54,46,69,57 is 1.
Lets's calculate LCM of 39,31,12,62
2 | 39, 31, 12, 62 |
3 | 39, 31, 6, 31 |
31 | 13, 31, 2, 31 |
13, 1, 2, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 31 x 13 x 1 x 2 x 1 = 4836
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4836
Therefore, the GCF of Fractions 54/39,46/31,69/12,57/62 is 1/4836
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 39,31,12,62 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,31,12,62) = 1
common factors(in case of two or more numbers have common factors) = 186
GCF(39,31,12,62) x common factors =1 x 186 = 186
LCM(39,31,12,62) = ( 39 × 31 × 12 × 62 ) / 186
LCM(39,31,12,62) = 899496 / 186
LCM(39,31,12,62) = 4836
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 54/39, 46/31, 69/12, 57/62?
Answer: GCF of Numerators as per given numbers 54/39, 46/31, 69/12, 57/62 is
GCF of Numerators i.e. for 54,46,69,57 is 1
LCM of denominators i.e. for 39,31,12,62 is 4836.
Thus, GCF of Fractions is 1/4836.Finally, GCF of Fractions for 54/39, 46/31, 69/12, 57/62 is 1/4836.