Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 18/57,90/57,25/72,71/63
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 18,90,25,71
Greatest Common Factor of Numerators i.e. GCF of 18,90,25,71 is 1 .
LCM of Denominators means LCM of 57,57,72,63 as per the given fractions.
LCM of 57,57,72,63 is 9576 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 18,90,25,71
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Greatest Common Factor
We found the factors 18,90,25,71 . The biggest common factor number is the GCF number.
So the greatest common factor 18,90,25,71 is 1.
Lets's calculate LCM of 57,57,72,63
3 | 57, 57, 72, 63 |
3 | 19, 19, 24, 21 |
19 | 19, 19, 8, 7 |
1, 1, 8, 7 |
∴ So the LCM of the given numbers is 3 x 3 x 19 x 1 x 1 x 8 x 7 = 9576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9576
Therefore, the GCF of Fractions 18/57,90/57,25/72,71/63 is 1/9576
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 57,57,72,63 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,57,72,63) = 3
common factors(in case of two or more numbers have common factors) = 513
GCF(57,57,72,63) x common factors =3 x 513 = 1539
LCM(57,57,72,63) = ( 57 × 57 × 72 × 63 ) / 1539
LCM(57,57,72,63) = 14737464 / 1539
LCM(57,57,72,63) = 9576
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 18/57, 90/57, 25/72, 71/63?
Answer: GCF of Numerators as per given numbers 18/57, 90/57, 25/72, 71/63 is
GCF of Numerators i.e. for 18,90,25,71 is 1
LCM of denominators i.e. for 57,57,72,63 is 9576.
Thus, GCF of Fractions is 1/9576.Finally, GCF of Fractions for 18/57, 90/57, 25/72, 71/63 is 1/9576.