Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 46/171,309/114,322/162
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 46,309,322
Greatest Common Factor of Numerators i.e. GCF of 46,309,322 is 1 .
LCM of Denominators means LCM of 171,114,162 as per the given fractions.
LCM of 171,114,162 is 3078 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 46,309,322
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 309
List of positive integer factors of 309 that divides 309 without a remainder.
1,3,103,309
Factors of 322
List of positive integer factors of 322 that divides 322 without a remainder.
1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 46,309,322 . The biggest common factor number is the GCF number.
So the greatest common factor 46,309,322 is 1.
Lets's calculate LCM of 171,114,162
2 | 171, 114, 162 |
3 | 171, 57, 81 |
3 | 19, 57, 27 |
19 | 19, 19, 9 |
1, 1, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 19 x 1 x 1 x 9 = 3078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3078
Therefore, the GCF of Fractions 46/171,309/114,322/162 is 1/3078
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 171,114,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,114,162) = 3
common factors(in case of two or more numbers have common factors) = 342
GCF(171,114,162) x common factors =3 x 342 = 1026
LCM(171,114,162) = ( 171 × 114 × 162 ) / 1026
LCM(171,114,162) = 3158028 / 1026
LCM(171,114,162) = 3078
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 46/171, 309/114, 322/162?
Answer: GCF of Numerators as per given numbers 46/171, 309/114, 322/162 is
GCF of Numerators i.e. for 46,309,322 is 1
LCM of denominators i.e. for 171,114,162 is 3078.
Thus, GCF of Fractions is 1/3078.Finally, GCF of Fractions for 46/171, 309/114, 322/162 is 1/3078.