Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 99/51,71/84,705/204
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 99,71,705
Greatest Common Factor of Numerators i.e. GCF of 99,71,705 is 1 .
LCM of Denominators means LCM of 51,84,204 as per the given fractions.
LCM of 51,84,204 is 1428 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 99,71,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 705
List of positive integer factors of 705 that divides 705 without a remainder.
1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 99,71,705 . The biggest common factor number is the GCF number.
So the greatest common factor 99,71,705 is 1.
Lets's calculate LCM of 51,84,204
2 | 51, 84, 204 |
2 | 51, 42, 102 |
3 | 51, 21, 51 |
17 | 17, 7, 17 |
1, 7, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 1 x 7 x 1 = 1428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1428
Therefore, the GCF of Fractions 99/51,71/84,705/204 is 1/1428
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 51,84,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,84,204) = 3
common factors(in case of two or more numbers have common factors) = 204
GCF(51,84,204) x common factors =3 x 204 = 612
LCM(51,84,204) = ( 51 × 84 × 204 ) / 612
LCM(51,84,204) = 873936 / 612
LCM(51,84,204) = 1428
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 99/51, 71/84, 705/204?
Answer: GCF of Numerators as per given numbers 99/51, 71/84, 705/204 is
GCF of Numerators i.e. for 99,71,705 is 1
LCM of denominators i.e. for 51,84,204 is 1428.
Thus, GCF of Fractions is 1/1428.Finally, GCF of Fractions for 99/51, 71/84, 705/204 is 1/1428.