Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 39/51,14/19,51/18,74/153
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 39,14,51,74
Greatest Common Factor of Numerators i.e. GCF of 39,14,51,74 is 1 .
LCM of Denominators means LCM of 51,19,18,153 as per the given fractions.
LCM of 51,19,18,153 is 5814 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 39,14,51,74
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Greatest Common Factor
We found the factors 39,14,51,74 . The biggest common factor number is the GCF number.
So the greatest common factor 39,14,51,74 is 1.
Lets's calculate LCM of 51,19,18,153
3 | 51, 19, 18, 153 |
3 | 17, 19, 6, 51 |
17 | 17, 19, 2, 17 |
1, 19, 2, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 17 x 1 x 19 x 2 x 1 = 5814
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5814
Therefore, the GCF of Fractions 39/51,14/19,51/18,74/153 is 1/5814
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 51,19,18,153 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,19,18,153) = 1
common factors(in case of two or more numbers have common factors) = 459
GCF(51,19,18,153) x common factors =1 x 459 = 459
LCM(51,19,18,153) = ( 51 × 19 × 18 × 153 ) / 459
LCM(51,19,18,153) = 2668626 / 459
LCM(51,19,18,153) = 5814
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 39/51, 14/19, 51/18, 74/153?
Answer: GCF of Numerators as per given numbers 39/51, 14/19, 51/18, 74/153 is
GCF of Numerators i.e. for 39,14,51,74 is 1
LCM of denominators i.e. for 51,19,18,153 is 5814.
Thus, GCF of Fractions is 1/5814.Finally, GCF of Fractions for 39/51, 14/19, 51/18, 74/153 is 1/5814.