Use our free GCF of Fractions Calculator tool to compute the GCF of 257/814, 416/996 i.e 1/405372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 257/814, 416/996.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 257/814,416/996
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 257/814,416/996, numerators are 257,416
Denominators are 814,996
The GCF of 257,416 is 1 .
LCM of 814,996 is 405372.
The greatest common factor of 257/814,416/996 = [GCF of 257,416]/[LCM of 814,996]= 1/405372
Therefore, the GCF of 257/814,416/996 is 1/405372.
To find the highest common factor of 257,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 257 are 1, 257
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 257,416 is 1.
Lets's calculate GCF of 257,416
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 257
:1,257
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 257,416 . The biggest common factor number is the GCF number.
So the greatest common factor 257,416 is 1.
Lets's calculate LCM of 814,996
2 | 814, 996 |
407, 498 |
∴ So the LCM of the given numbers is 2 x 407 x 498 = 405372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/405372
Therefore, the GCF of Fractions 257/814,416/996 is 1/405372
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 814,996 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,996) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(814,996) x common factors =2 x 1 = 2
LCM(814,996) = ( 814 × 996 ) / 2
LCM(814,996) = 810744 / 2
LCM(814,996) = 405372
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 257,416?
The HCF of 257,416 is 1
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 257/814, 416/996?
Answer: GCF of Numerators as per given numbers 257/814, 416/996 is
GCF of Numerators i.e. for 257,416 is 1
LCM of denominators i.e. for 814,996 is 405372.
Thus, GCF of Fractions is 1/405372.Finally, GCF of Fractions for 257/814, 416/996 is 1/405372.