Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 29/84,20/77,43/38,84/969
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 29,20,43,84
Greatest Common Factor of Numerators i.e. GCF of 29,20,43,84 is 1 .
LCM of Denominators means LCM of 84,77,38,969 as per the given fractions.
LCM of 84,77,38,969 is 298452 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 29,20,43,84
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 29
List of positive integer factors of 29 that divides 29 without a remainder.
1,29
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Greatest Common Factor
We found the factors 29,20,43,84 . The biggest common factor number is the GCF number.
So the greatest common factor 29,20,43,84 is 1.
Lets's calculate LCM of 84,77,38,969
2 | 84, 77, 38, 969 |
3 | 42, 77, 19, 969 |
7 | 14, 77, 19, 323 |
19 | 2, 11, 19, 323 |
2, 11, 1, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 19 x 2 x 11 x 1 x 17 = 298452
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/298452
Therefore, the GCF of Fractions 29/84,20/77,43/38,84/969 is 1/298452
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 84,77,38,969 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,77,38,969) = 1
common factors(in case of two or more numbers have common factors) = 798
GCF(84,77,38,969) x common factors =1 x 798 = 798
LCM(84,77,38,969) = ( 84 × 77 × 38 × 969 ) / 798
LCM(84,77,38,969) = 238164696 / 798
LCM(84,77,38,969) = 298452
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 29/84, 20/77, 43/38, 84/969?
Answer: GCF of Numerators as per given numbers 29/84, 20/77, 43/38, 84/969 is
GCF of Numerators i.e. for 29,20,43,84 is 1
LCM of denominators i.e. for 84,77,38,969 is 298452.
Thus, GCF of Fractions is 1/298452.Finally, GCF of Fractions for 29/84, 20/77, 43/38, 84/969 is 1/298452.