Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1656/42,2070/181
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 1656,2070
Greatest Common Factor of Numerators i.e. GCF of 1656,2070 is 414 .
LCM of Denominators means LCM of 42,181 as per the given fractions.
LCM of 42,181 is 7602 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 1656,2070
2 | 1656, 2070 |
3 | 828, 1035 |
3 | 276, 345 |
23 | 92, 115 |
4, 5 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 23 = 414
Factors of 1656
List of positive integer factors of 1656 that divides 1656 without a remainder.
1,2,3,4,6,8,9,12,18,23,24,36,46,69,72,92,138,184,207,276,414,552,828,1656
Factors of 2070
List of positive integer factors of 2070 that divides 2070 without a remainder.
1,2,3,5,6,9,10,15,18,23,30,45,46,69,90,115,138,207,230,345,414,690,1035,2070
Greatest Common Factor
We found the factors 1656,2070 . The biggest common factor number is the GCF number.
So the greatest common factor 1656,2070 is 414.
Lets's calculate LCM of 42,181
Given numbers has no common factors except 1. So, there LCM is their product i.e 7602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 414/7602
Therefore, the GCF of Fractions 1656/42,2070/181 is 414/7602
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 42,181 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,181) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(42,181) x common factors =1 x 1 = 1
LCM(42,181) = ( 42 × 181 ) / 1
LCM(42,181) = 7602 / 1
LCM(42,181) = 7602
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 1656/42, 2070/181?
Answer: GCF of Numerators as per given numbers 1656/42, 2070/181 is
GCF of Numerators i.e. for 1656,2070 is 414
LCM of denominators i.e. for 42,181 is 7602.
Thus, GCF of Fractions is 414/7602.Finally, GCF of Fractions for 1656/42, 2070/181 is 414/7602.