Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 83/27,79/68,76/45,89/208
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 83,79,76,89
Greatest Common Factor of Numerators i.e. GCF of 83,79,76,89 is 1 .
LCM of Denominators means LCM of 27,68,45,208 as per the given fractions.
LCM of 27,68,45,208 is 477360 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 83,79,76,89
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 79
List of positive integer factors of 79 that divides 79 without a remainder.
1,79
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Greatest Common Factor
We found the factors 83,79,76,89 . The biggest common factor number is the GCF number.
So the greatest common factor 83,79,76,89 is 1.
Lets's calculate LCM of 27,68,45,208
2 | 27, 68, 45, 208 |
2 | 27, 34, 45, 104 |
3 | 27, 17, 45, 52 |
3 | 9, 17, 15, 52 |
3, 17, 5, 52 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 17 x 5 x 52 = 477360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/477360
Therefore, the GCF of Fractions 83/27,79/68,76/45,89/208 is 1/477360
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 27,68,45,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,68,45,208) = 1
common factors(in case of two or more numbers have common factors) = 36
GCF(27,68,45,208) x common factors =1 x 36 = 36
LCM(27,68,45,208) = ( 27 × 68 × 45 × 208 ) / 36
LCM(27,68,45,208) = 17184960 / 36
LCM(27,68,45,208) = 477360
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 83/27, 79/68, 76/45, 89/208?
Answer: GCF of Numerators as per given numbers 83/27, 79/68, 76/45, 89/208 is
GCF of Numerators i.e. for 83,79,76,89 is 1
LCM of denominators i.e. for 27,68,45,208 is 477360.
Thus, GCF of Fractions is 1/477360.Finally, GCF of Fractions for 83/27, 79/68, 76/45, 89/208 is 1/477360.