Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/105,753/421
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 84,753
Greatest Common Factor of Numerators i.e. GCF of 84,753 is 3 .
LCM of Denominators means LCM of 105,421 as per the given fractions.
LCM of 105,421 is 44205 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 84,753
3 | 84, 753 |
28, 251 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 753
List of positive integer factors of 753 that divides 753 without a remainder.
1,3,251,753
Greatest Common Factor
We found the factors 84,753 . The biggest common factor number is the GCF number.
So the greatest common factor 84,753 is 3.
Lets's calculate LCM of 105,421
Given numbers has no common factors except 1. So, there LCM is their product i.e 44205
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/44205
Therefore, the GCF of Fractions 84/105,753/421 is 3/44205
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 105,421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(105,421) x common factors =1 x 1 = 1
LCM(105,421) = ( 105 × 421 ) / 1
LCM(105,421) = 44205 / 1
LCM(105,421) = 44205
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 84/105, 753/421?
Answer: GCF of Numerators as per given numbers 84/105, 753/421 is
GCF of Numerators i.e. for 84,753 is 3
LCM of denominators i.e. for 105,421 is 44205.
Thus, GCF of Fractions is 3/44205.Finally, GCF of Fractions for 84/105, 753/421 is 3/44205.