Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8614/32,3172/512
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 8614,3172
Greatest Common Factor of Numerators i.e. GCF of 8614,3172 is 2 .
LCM of Denominators means LCM of 32,512 as per the given fractions.
LCM of 32,512 is 512 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 8614,3172
2 | 8614, 3172 |
4307, 1586 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 8614
List of positive integer factors of 8614 that divides 8614 without a remainder.
1,2,59,73,118,146,4307,8614
Factors of 3172
List of positive integer factors of 3172 that divides 3172 without a remainder.
1,2,4,13,26,52,61,122,244,793,1586,3172
Greatest Common Factor
We found the factors 8614,3172 . The biggest common factor number is the GCF number.
So the greatest common factor 8614,3172 is 2.
Lets's calculate LCM of 32,512
2 | 32, 512 |
2 | 16, 256 |
2 | 8, 128 |
2 | 4, 64 |
2 | 2, 32 |
1, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 16 = 512
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/512
Therefore, the GCF of Fractions 8614/32,3172/512 is 2/512
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 32,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,512) = 32
common factors(in case of two or more numbers have common factors) = 1
GCF(32,512) x common factors =32 x 1 = 32
LCM(32,512) = ( 32 × 512 ) / 32
LCM(32,512) = 16384 / 32
LCM(32,512) = 512
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 8614/32, 3172/512?
Answer: GCF of Numerators as per given numbers 8614/32, 3172/512 is
GCF of Numerators i.e. for 8614,3172 is 2
LCM of denominators i.e. for 32,512 is 512.
Thus, GCF of Fractions is 2/512.Finally, GCF of Fractions for 8614/32, 3172/512 is 2/512.