Use our free GCF of Fractions Calculator tool to compute the GCF of 207/271, 414/254 i.e 207/68834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 207/271, 414/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 207/271,414/254
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 207/271,414/254, numerators are 207,414
Denominators are 271,254
The GCF of 207,414 is 207 .
LCM of 271,254 is 68834.
The greatest common factor of 207/271,414/254 = [GCF of 207,414]/[LCM of 271,254]= 207/68834
Therefore, the GCF of 207/271,414/254 is 207/68834.
To find the highest common factor of 207,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 207 are 1, 3, 9, 23, 69, 207
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 207,414 is 207.
Lets's calculate GCF of 207,414
3 | 207, 414 |
3 | 69, 138 |
23 | 23, 46 |
1, 2 |
∴ So the GCF of the given numbers is 3 x 3 x 23 = 207
Now, list down the factors of 207
:1,3,9,23,69,207
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 207,414 . The biggest common factor number is the GCF number.
So the greatest common factor 207,414 is 207.
Lets's calculate LCM of 271,254
Given numbers has no common factors except 1. So, there LCM is their product i.e 68834
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 207/68834
Therefore, the GCF of Fractions 207/271,414/254 is 207/68834
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 271,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(271,254) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(271,254) x common factors =1 x 1 = 1
LCM(271,254) = ( 271 × 254 ) / 1
LCM(271,254) = 68834 / 1
LCM(271,254) = 68834
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 207,414?
The HCF of 207,414 is 207
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 207/271, 414/254?
Answer: GCF of Numerators as per given numbers 207/271, 414/254 is
GCF of Numerators i.e. for 207,414 is 207
LCM of denominators i.e. for 271,254 is 68834.
Thus, GCF of Fractions is 207/68834.Finally, GCF of Fractions for 207/271, 414/254 is 207/68834.