Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/52,25/57,67/35,15/21
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 65,25,67,15
Greatest Common Factor of Numerators i.e. GCF of 65,25,67,15 is 1 .
LCM of Denominators means LCM of 52,57,35,21 as per the given fractions.
LCM of 52,57,35,21 is 103740 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 65,25,67,15
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Greatest Common Factor
We found the factors 65,25,67,15 . The biggest common factor number is the GCF number.
So the greatest common factor 65,25,67,15 is 1.
Lets's calculate LCM of 52,57,35,21
3 | 52, 57, 35, 21 |
7 | 52, 19, 35, 7 |
52, 19, 5, 1 |
∴ So the LCM of the given numbers is 3 x 7 x 52 x 19 x 5 x 1 = 103740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/103740
Therefore, the GCF of Fractions 65/52,25/57,67/35,15/21 is 1/103740
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 52,57,35,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,57,35,21) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(52,57,35,21) x common factors =1 x 21 = 21
LCM(52,57,35,21) = ( 52 × 57 × 35 × 21 ) / 21
LCM(52,57,35,21) = 2178540 / 21
LCM(52,57,35,21) = 103740
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 65/52, 25/57, 67/35, 15/21?
Answer: GCF of Numerators as per given numbers 65/52, 25/57, 67/35, 15/21 is
GCF of Numerators i.e. for 65,25,67,15 is 1
LCM of denominators i.e. for 52,57,35,21 is 103740.
Thus, GCF of Fractions is 1/103740.Finally, GCF of Fractions for 65/52, 25/57, 67/35, 15/21 is 1/103740.