Use our free GCF of Fractions Calculator tool to compute the GCF of 414/172, 213/270 i.e 3/23220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/172, 213/270.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/172,213/270
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 414/172,213/270, numerators are 414,213
Denominators are 172,270
The GCF of 414,213 is 3 .
LCM of 172,270 is 23220.
The greatest common factor of 414/172,213/270 = [GCF of 414,213]/[LCM of 172,270]= 3/23220
Therefore, the GCF of 414/172,213/270 is 3/23220.
To find the highest common factor of 414,213, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 213 are 1, 3, 71, 213
The HCF of 414,213 is 3.
Lets's calculate GCF of 414,213
3 | 414, 213 |
138, 71 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 213
:1,3,71,213
Greatest Common Factor
We found the factors 414,213 . The biggest common factor number is the GCF number.
So the greatest common factor 414,213 is 3.
Lets's calculate LCM of 172,270
2 | 172, 270 |
86, 135 |
∴ So the LCM of the given numbers is 2 x 86 x 135 = 23220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23220
Therefore, the GCF of Fractions 414/172,213/270 is 3/23220
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 172,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,270) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(172,270) x common factors =2 x 1 = 2
LCM(172,270) = ( 172 × 270 ) / 2
LCM(172,270) = 46440 / 2
LCM(172,270) = 23220
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 414,213?
The HCF of 414,213 is 3
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 414/172, 213/270?
Answer: GCF of Numerators as per given numbers 414/172, 213/270 is
GCF of Numerators i.e. for 414,213 is 3
LCM of denominators i.e. for 172,270 is 23220.
Thus, GCF of Fractions is 3/23220.Finally, GCF of Fractions for 414/172, 213/270 is 3/23220.