Use our free GCF of Fractions Calculator tool to compute the GCF of 513/628, 684/657 i.e 171/412596 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/628, 684/657.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 513/628,684/657
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 513/628,684/657, numerators are 513,684
Denominators are 628,657
The GCF of 513,684 is 171 .
LCM of 628,657 is 412596.
The greatest common factor of 513/628,684/657 = [GCF of 513,684]/[LCM of 628,657]= 171/412596
Therefore, the GCF of 513/628,684/657 is 171/412596.
To find the highest common factor of 513,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 513,684 is 171.
Lets's calculate GCF of 513,684
3 | 513, 684 |
3 | 171, 228 |
19 | 57, 76 |
3, 4 |
∴ So the GCF of the given numbers is 3 x 3 x 19 = 171
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 513,684 . The biggest common factor number is the GCF number.
So the greatest common factor 513,684 is 171.
Lets's calculate LCM of 628,657
Given numbers has no common factors except 1. So, there LCM is their product i.e 412596
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 171/412596
Therefore, the GCF of Fractions 513/628,684/657 is 171/412596
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 628,657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(628,657) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(628,657) x common factors =1 x 1 = 1
LCM(628,657) = ( 628 × 657 ) / 1
LCM(628,657) = 412596 / 1
LCM(628,657) = 412596
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 513,684?
The HCF of 513,684 is 171
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 513/628, 684/657?
Answer: GCF of Numerators as per given numbers 513/628, 684/657 is
GCF of Numerators i.e. for 513,684 is 171
LCM of denominators i.e. for 628,657 is 412596.
Thus, GCF of Fractions is 171/412596.Finally, GCF of Fractions for 513/628, 684/657 is 171/412596.