Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 74/12,26/66,73/65,35/85
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 74,26,73,35
Greatest Common Factor of Numerators i.e. GCF of 74,26,73,35 is 1 .
LCM of Denominators means LCM of 12,66,65,85 as per the given fractions.
LCM of 12,66,65,85 is 145860 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 74,26,73,35
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 26
List of positive integer factors of 26 that divides 26 without a remainder.
1,2,13,26
Factors of 73
List of positive integer factors of 73 that divides 73 without a remainder.
1,73
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Greatest Common Factor
We found the factors 74,26,73,35 . The biggest common factor number is the GCF number.
So the greatest common factor 74,26,73,35 is 1.
Lets's calculate LCM of 12,66,65,85
2 | 12, 66, 65, 85 |
3 | 6, 33, 65, 85 |
5 | 2, 11, 65, 85 |
2, 11, 13, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 2 x 11 x 13 x 17 = 145860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/145860
Therefore, the GCF of Fractions 74/12,26/66,73/65,35/85 is 1/145860
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 12,66,65,85 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,66,65,85) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(12,66,65,85) x common factors =1 x 30 = 30
LCM(12,66,65,85) = ( 12 × 66 × 65 × 85 ) / 30
LCM(12,66,65,85) = 4375800 / 30
LCM(12,66,65,85) = 145860
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 74/12, 26/66, 73/65, 35/85?
Answer: GCF of Numerators as per given numbers 74/12, 26/66, 73/65, 35/85 is
GCF of Numerators i.e. for 74,26,73,35 is 1
LCM of denominators i.e. for 12,66,65,85 is 145860.
Thus, GCF of Fractions is 1/145860.Finally, GCF of Fractions for 74/12, 26/66, 73/65, 35/85 is 1/145860.