Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/21,83/27,27/39,79/210
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 77,83,27,79
Greatest Common Factor of Numerators i.e. GCF of 77,83,27,79 is 1 .
LCM of Denominators means LCM of 21,27,39,210 as per the given fractions.
LCM of 21,27,39,210 is 24570 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 77,83,27,79
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 79
List of positive integer factors of 79 that divides 79 without a remainder.
1,79
Greatest Common Factor
We found the factors 77,83,27,79 . The biggest common factor number is the GCF number.
So the greatest common factor 77,83,27,79 is 1.
Lets's calculate LCM of 21,27,39,210
3 | 21, 27, 39, 210 |
7 | 7, 9, 13, 70 |
1, 9, 13, 10 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 9 x 13 x 10 = 24570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24570
Therefore, the GCF of Fractions 77/21,83/27,27/39,79/210 is 1/24570
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 21,27,39,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,27,39,210) = 3
common factors(in case of two or more numbers have common factors) = 63
GCF(21,27,39,210) x common factors =3 x 63 = 189
LCM(21,27,39,210) = ( 21 × 27 × 39 × 210 ) / 189
LCM(21,27,39,210) = 4643730 / 189
LCM(21,27,39,210) = 24570
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 77/21, 83/27, 27/39, 79/210?
Answer: GCF of Numerators as per given numbers 77/21, 83/27, 27/39, 79/210 is
GCF of Numerators i.e. for 77,83,27,79 is 1
LCM of denominators i.e. for 21,27,39,210 is 24570.
Thus, GCF of Fractions is 1/24570.Finally, GCF of Fractions for 77/21, 83/27, 27/39, 79/210 is 1/24570.