Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 15/68,86/23,69/62,78/70
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 15,86,69,78
Greatest Common Factor of Numerators i.e. GCF of 15,86,69,78 is 1 .
LCM of Denominators means LCM of 68,23,62,70 as per the given fractions.
LCM of 68,23,62,70 is 1696940 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 15,86,69,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 15,86,69,78 . The biggest common factor number is the GCF number.
So the greatest common factor 15,86,69,78 is 1.
Lets's calculate LCM of 68,23,62,70
2 | 68, 23, 62, 70 |
34, 23, 31, 35 |
∴ So the LCM of the given numbers is 2 x 34 x 23 x 31 x 35 = 1696940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1696940
Therefore, the GCF of Fractions 15/68,86/23,69/62,78/70 is 1/1696940
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 68,23,62,70 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,23,62,70) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(68,23,62,70) x common factors =1 x 4 = 4
LCM(68,23,62,70) = ( 68 × 23 × 62 × 70 ) / 4
LCM(68,23,62,70) = 6787760 / 4
LCM(68,23,62,70) = 1696940
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 15/68, 86/23, 69/62, 78/70?
Answer: GCF of Numerators as per given numbers 15/68, 86/23, 69/62, 78/70 is
GCF of Numerators i.e. for 15,86,69,78 is 1
LCM of denominators i.e. for 68,23,62,70 is 1696940.
Thus, GCF of Fractions is 1/1696940.Finally, GCF of Fractions for 15/68, 86/23, 69/62, 78/70 is 1/1696940.