Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 705/18,278/1709
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 705,278
Greatest Common Factor of Numerators i.e. GCF of 705,278 is 1 .
LCM of Denominators means LCM of 18,1709 as per the given fractions.
LCM of 18,1709 is 30762 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 705,278
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 705
List of positive integer factors of 705 that divides 705 without a remainder.
1,3,5,15,47,141,235,705
Factors of 278
List of positive integer factors of 278 that divides 278 without a remainder.
1,2,139,278
Greatest Common Factor
We found the factors 705,278 . The biggest common factor number is the GCF number.
So the greatest common factor 705,278 is 1.
Lets's calculate LCM of 18,1709
Given numbers has no common factors except 1. So, there LCM is their product i.e 30762
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30762
Therefore, the GCF of Fractions 705/18,278/1709 is 1/30762
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 18,1709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,1709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(18,1709) x common factors =1 x 1 = 1
LCM(18,1709) = ( 18 × 1709 ) / 1
LCM(18,1709) = 30762 / 1
LCM(18,1709) = 30762
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 705/18, 278/1709?
Answer: GCF of Numerators as per given numbers 705/18, 278/1709 is
GCF of Numerators i.e. for 705,278 is 1
LCM of denominators i.e. for 18,1709 is 30762.
Thus, GCF of Fractions is 1/30762.Finally, GCF of Fractions for 705/18, 278/1709 is 1/30762.