Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/12,45/22,385/628
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 65,45,385
Greatest Common Factor of Numerators i.e. GCF of 65,45,385 is 5 .
LCM of Denominators means LCM of 12,22,628 as per the given fractions.
LCM of 12,22,628 is 20724 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 65,45,385
5 | 65, 45, 385 |
13, 9, 77 |
∴ So the GCF of the given numbers is 5 = 5
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 385
List of positive integer factors of 385 that divides 385 without a remainder.
1,5,7,11,35,55,77,385
Greatest Common Factor
We found the factors 65,45,385 . The biggest common factor number is the GCF number.
So the greatest common factor 65,45,385 is 5.
Lets's calculate LCM of 12,22,628
2 | 12, 22, 628 |
2 | 6, 11, 314 |
3, 11, 157 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 11 x 157 = 20724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/20724
Therefore, the GCF of Fractions 65/12,45/22,385/628 is 5/20724
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 12,22,628 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,22,628) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(12,22,628) x common factors =2 x 4 = 8
LCM(12,22,628) = ( 12 × 22 × 628 ) / 8
LCM(12,22,628) = 165792 / 8
LCM(12,22,628) = 20724
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 65/12, 45/22, 385/628?
Answer: GCF of Numerators as per given numbers 65/12, 45/22, 385/628 is
GCF of Numerators i.e. for 65,45,385 is 5
LCM of denominators i.e. for 12,22,628 is 20724.
Thus, GCF of Fractions is 5/20724.Finally, GCF of Fractions for 65/12, 45/22, 385/628 is 5/20724.