Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/75,47/83,49/21,840/13
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 17,47,49,840
Greatest Common Factor of Numerators i.e. GCF of 17,47,49,840 is 1 .
LCM of Denominators means LCM of 75,83,21,13 as per the given fractions.
LCM of 75,83,21,13 is 566475 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 17,47,49,840
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Factors of 47
List of positive integer factors of 47 that divides 47 without a remainder.
1,47
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 840
List of positive integer factors of 840 that divides 840 without a remainder.
1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 17,47,49,840 . The biggest common factor number is the GCF number.
So the greatest common factor 17,47,49,840 is 1.
Lets's calculate LCM of 75,83,21,13
3 | 75, 83, 21, 13 |
25, 83, 7, 13 |
∴ So the LCM of the given numbers is 3 x 25 x 83 x 7 x 13 = 566475
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/566475
Therefore, the GCF of Fractions 17/75,47/83,49/21,840/13 is 1/566475
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 75,83,21,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,83,21,13) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(75,83,21,13) x common factors =1 x 3 = 3
LCM(75,83,21,13) = ( 75 × 83 × 21 × 13 ) / 3
LCM(75,83,21,13) = 1699425 / 3
LCM(75,83,21,13) = 566475
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 17/75, 47/83, 49/21, 840/13?
Answer: GCF of Numerators as per given numbers 17/75, 47/83, 49/21, 840/13 is
GCF of Numerators i.e. for 17,47,49,840 is 1
LCM of denominators i.e. for 75,83,21,13 is 566475.
Thus, GCF of Fractions is 1/566475.Finally, GCF of Fractions for 17/75, 47/83, 49/21, 840/13 is 1/566475.