Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/99,74/68,216/39
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 84,74,216
Greatest Common Factor of Numerators i.e. GCF of 84,74,216 is 2 .
LCM of Denominators means LCM of 99,68,39 as per the given fractions.
LCM of 99,68,39 is 87516 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 84,74,216
2 | 84, 74, 216 |
42, 37, 108 |
∴ So the GCF of the given numbers is 2 = 2
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
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 216
List of positive integer factors of 216 that divides 216 without a remainder.
1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 84,74,216 . The biggest common factor number is the GCF number.
So the greatest common factor 84,74,216 is 2.
Lets's calculate LCM of 99,68,39
3 | 99, 68, 39 |
33, 68, 13 |
∴ So the LCM of the given numbers is 3 x 33 x 68 x 13 = 87516
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/87516
Therefore, the GCF of Fractions 84/99,74/68,216/39 is 2/87516
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 99,68,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(99,68,39) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(99,68,39) x common factors =1 x 3 = 3
LCM(99,68,39) = ( 99 × 68 × 39 ) / 3
LCM(99,68,39) = 262548 / 3
LCM(99,68,39) = 87516
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 84/99, 74/68, 216/39?
Answer: GCF of Numerators as per given numbers 84/99, 74/68, 216/39 is
GCF of Numerators i.e. for 84,74,216 is 2
LCM of denominators i.e. for 99,68,39 is 87516.
Thus, GCF of Fractions is 2/87516.Finally, GCF of Fractions for 84/99, 74/68, 216/39 is 2/87516.