Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/81,207/7369
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 414,207
Greatest Common Factor of Numerators i.e. GCF of 414,207 is 207 .
LCM of Denominators means LCM of 81,7369 as per the given fractions.
LCM of 81,7369 is 596889 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 414,207
3 | 414, 207 |
3 | 138, 69 |
23 | 46, 23 |
2, 1 |
∴ So the GCF of the given numbers is 3 x 3 x 23 = 207
Factors of 414
List of positive integer factors of 414 that divides 414 without a remainder.
1,2,3,6,9,18,23,46,69,138,207,414
Factors of 207
List of positive integer factors of 207 that divides 207 without a remainder.
1,3,9,23,69,207
Greatest Common Factor
We found the factors 414,207 . The biggest common factor number is the GCF number.
So the greatest common factor 414,207 is 207.
Lets's calculate LCM of 81,7369
Given numbers has no common factors except 1. So, there LCM is their product i.e 596889
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 207/596889
Therefore, the GCF of Fractions 414/81,207/7369 is 207/596889
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 81,7369 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,7369) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(81,7369) x common factors =1 x 1 = 1
LCM(81,7369) = ( 81 × 7369 ) / 1
LCM(81,7369) = 596889 / 1
LCM(81,7369) = 596889
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 414/81, 207/7369?
Answer: GCF of Numerators as per given numbers 414/81, 207/7369 is
GCF of Numerators i.e. for 414,207 is 207
LCM of denominators i.e. for 81,7369 is 596889.
Thus, GCF of Fractions is 207/596889.Finally, GCF of Fractions for 414/81, 207/7369 is 207/596889.