Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 51/58,99/60,24/37,42/32
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 51,99,24,42
Greatest Common Factor of Numerators i.e. GCF of 51,99,24,42 is 3 .
LCM of Denominators means LCM of 58,60,37,32 as per the given fractions.
LCM of 58,60,37,32 is 515040 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 51,99,24,42
3 | 51, 99, 24, 42 |
17, 33, 8, 14 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 51,99,24,42 . The biggest common factor number is the GCF number.
So the greatest common factor 51,99,24,42 is 3.
Lets's calculate LCM of 58,60,37,32
2 | 58, 60, 37, 32 |
2 | 29, 30, 37, 16 |
29, 15, 37, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 29 x 15 x 37 x 8 = 515040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/515040
Therefore, the GCF of Fractions 51/58,99/60,24/37,42/32 is 3/515040
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 58,60,37,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,60,37,32) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(58,60,37,32) x common factors =1 x 8 = 8
LCM(58,60,37,32) = ( 58 × 60 × 37 × 32 ) / 8
LCM(58,60,37,32) = 4120320 / 8
LCM(58,60,37,32) = 515040
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 51/58, 99/60, 24/37, 42/32?
Answer: GCF of Numerators as per given numbers 51/58, 99/60, 24/37, 42/32 is
GCF of Numerators i.e. for 51,99,24,42 is 3
LCM of denominators i.e. for 58,60,37,32 is 515040.
Thus, GCF of Fractions is 3/515040.Finally, GCF of Fractions for 51/58, 99/60, 24/37, 42/32 is 3/515040.