Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 682/31,430/1739
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 682,430
Greatest Common Factor of Numerators i.e. GCF of 682,430 is 2 .
LCM of Denominators means LCM of 31,1739 as per the given fractions.
LCM of 31,1739 is 53909 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 682,430
2 | 682, 430 |
341, 215 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 682
List of positive integer factors of 682 that divides 682 without a remainder.
1,2,11,22,31,62,341,682
Factors of 430
List of positive integer factors of 430 that divides 430 without a remainder.
1,2,5,10,43,86,215,430
Greatest Common Factor
We found the factors 682,430 . The biggest common factor number is the GCF number.
So the greatest common factor 682,430 is 2.
Lets's calculate LCM of 31,1739
Given numbers has no common factors except 1. So, there LCM is their product i.e 53909
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/53909
Therefore, the GCF of Fractions 682/31,430/1739 is 2/53909
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 31,1739 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,1739) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,1739) x common factors =1 x 1 = 1
LCM(31,1739) = ( 31 × 1739 ) / 1
LCM(31,1739) = 53909 / 1
LCM(31,1739) = 53909
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 682/31, 430/1739?
Answer: GCF of Numerators as per given numbers 682/31, 430/1739 is
GCF of Numerators i.e. for 682,430 is 2
LCM of denominators i.e. for 31,1739 is 53909.
Thus, GCF of Fractions is 2/53909.Finally, GCF of Fractions for 682/31, 430/1739 is 2/53909.