Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/98,32/65,15/87,83/315
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 45,32,15,83
Greatest Common Factor of Numerators i.e. GCF of 45,32,15,83 is 1 .
LCM of Denominators means LCM of 98,65,87,315 as per the given fractions.
LCM of 98,65,87,315 is 1662570 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 45,32,15,83
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Greatest Common Factor
We found the factors 45,32,15,83 . The biggest common factor number is the GCF number.
So the greatest common factor 45,32,15,83 is 1.
Lets's calculate LCM of 98,65,87,315
3 | 98, 65, 87, 315 |
5 | 98, 65, 29, 105 |
7 | 98, 13, 29, 21 |
14, 13, 29, 3 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 14 x 13 x 29 x 3 = 1662570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1662570
Therefore, the GCF of Fractions 45/98,32/65,15/87,83/315 is 1/1662570
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 98,65,87,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(98,65,87,315) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(98,65,87,315) x common factors =1 x 105 = 105
LCM(98,65,87,315) = ( 98 × 65 × 87 × 315 ) / 105
LCM(98,65,87,315) = 174569850 / 105
LCM(98,65,87,315) = 1662570
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 45/98, 32/65, 15/87, 83/315?
Answer: GCF of Numerators as per given numbers 45/98, 32/65, 15/87, 83/315 is
GCF of Numerators i.e. for 45,32,15,83 is 1
LCM of denominators i.e. for 98,65,87,315 is 1662570.
Thus, GCF of Fractions is 1/1662570.Finally, GCF of Fractions for 45/98, 32/65, 15/87, 83/315 is 1/1662570.