Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/61,99/51,69/70,68/85
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 23,99,69,68
Greatest Common Factor of Numerators i.e. GCF of 23,99,69,68 is 1 .
LCM of Denominators means LCM of 61,51,70,85 as per the given fractions.
LCM of 61,51,70,85 is 217770 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 23,99,69,68
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Greatest Common Factor
We found the factors 23,99,69,68 . The biggest common factor number is the GCF number.
So the greatest common factor 23,99,69,68 is 1.
Lets's calculate LCM of 61,51,70,85
5 | 61, 51, 70, 85 |
17 | 61, 51, 14, 17 |
61, 3, 14, 1 |
∴ So the LCM of the given numbers is 5 x 17 x 61 x 3 x 14 x 1 = 217770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/217770
Therefore, the GCF of Fractions 23/61,99/51,69/70,68/85 is 1/217770
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 61,51,70,85 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,51,70,85) = 1
common factors(in case of two or more numbers have common factors) = 85
GCF(61,51,70,85) x common factors =1 x 85 = 85
LCM(61,51,70,85) = ( 61 × 51 × 70 × 85 ) / 85
LCM(61,51,70,85) = 18510450 / 85
LCM(61,51,70,85) = 217770
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 23/61, 99/51, 69/70, 68/85?
Answer: GCF of Numerators as per given numbers 23/61, 99/51, 69/70, 68/85 is
GCF of Numerators i.e. for 23,99,69,68 is 1
LCM of denominators i.e. for 61,51,70,85 is 217770.
Thus, GCF of Fractions is 1/217770.Finally, GCF of Fractions for 23/61, 99/51, 69/70, 68/85 is 1/217770.