Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 39/84,61/75,557/708
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 39,61,557
Greatest Common Factor of Numerators i.e. GCF of 39,61,557 is 1 .
LCM of Denominators means LCM of 84,75,708 as per the given fractions.
LCM of 84,75,708 is 123900 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 39,61,557
∴ 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 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 557
List of positive integer factors of 557 that divides 557 without a remainder.
1,557
Greatest Common Factor
We found the factors 39,61,557 . The biggest common factor number is the GCF number.
So the greatest common factor 39,61,557 is 1.
Lets's calculate LCM of 84,75,708
2 | 84, 75, 708 |
2 | 42, 75, 354 |
3 | 21, 75, 177 |
7, 25, 59 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 25 x 59 = 123900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/123900
Therefore, the GCF of Fractions 39/84,61/75,557/708 is 1/123900
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 84,75,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,75,708) = 3
common factors(in case of two or more numbers have common factors) = 12
GCF(84,75,708) x common factors =3 x 12 = 36
LCM(84,75,708) = ( 84 × 75 × 708 ) / 36
LCM(84,75,708) = 4460400 / 36
LCM(84,75,708) = 123900
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 39/84, 61/75, 557/708?
Answer: GCF of Numerators as per given numbers 39/84, 61/75, 557/708 is
GCF of Numerators i.e. for 39,61,557 is 1
LCM of denominators i.e. for 84,75,708 is 123900.
Thus, GCF of Fractions is 1/123900.Finally, GCF of Fractions for 39/84, 61/75, 557/708 is 1/123900.