Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/33,32/82,63/42,60/88
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 30,32,63,60
Greatest Common Factor of Numerators i.e. GCF of 30,32,63,60 is 1 .
LCM of Denominators means LCM of 33,82,42,88 as per the given fractions.
LCM of 33,82,42,88 is 75768 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 30,32,63,60
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1,3,7,9,21,63
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 30,32,63,60 . The biggest common factor number is the GCF number.
So the greatest common factor 30,32,63,60 is 1.
Lets's calculate LCM of 33,82,42,88
2 | 33, 82, 42, 88 |
3 | 33, 41, 21, 44 |
11 | 11, 41, 7, 44 |
1, 41, 7, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 1 x 41 x 7 x 4 = 75768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75768
Therefore, the GCF of Fractions 30/33,32/82,63/42,60/88 is 1/75768
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 33,82,42,88 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(33,82,42,88) = 1
common factors(in case of two or more numbers have common factors) = 132
GCF(33,82,42,88) x common factors =1 x 132 = 132
LCM(33,82,42,88) = ( 33 × 82 × 42 × 88 ) / 132
LCM(33,82,42,88) = 10001376 / 132
LCM(33,82,42,88) = 75768
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 30/33, 32/82, 63/42, 60/88?
Answer: GCF of Numerators as per given numbers 30/33, 32/82, 63/42, 60/88 is
GCF of Numerators i.e. for 30,32,63,60 is 1
LCM of denominators i.e. for 33,82,42,88 is 75768.
Thus, GCF of Fractions is 1/75768.Finally, GCF of Fractions for 30/33, 32/82, 63/42, 60/88 is 1/75768.