Use our free GCF of Fractions Calculator tool to compute the GCF of 537/994, 705/657 i.e 3/653058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 537/994, 705/657.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 537/994,705/657
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 537/994,705/657, numerators are 537,705
Denominators are 994,657
The GCF of 537,705 is 3 .
LCM of 994,657 is 653058.
The greatest common factor of 537/994,705/657 = [GCF of 537,705]/[LCM of 994,657]= 3/653058
Therefore, the GCF of 537/994,705/657 is 3/653058.
To find the highest common factor of 537,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 537 are 1, 3, 179, 537
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 537,705 is 3.
Lets's calculate GCF of 537,705
3 | 537, 705 |
179, 235 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 537
:1,3,179,537
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 537,705 . The biggest common factor number is the GCF number.
So the greatest common factor 537,705 is 3.
Lets's calculate LCM of 994,657
Given numbers has no common factors except 1. So, there LCM is their product i.e 653058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/653058
Therefore, the GCF of Fractions 537/994,705/657 is 3/653058
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 994,657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(994,657) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(994,657) x common factors =1 x 1 = 1
LCM(994,657) = ( 994 × 657 ) / 1
LCM(994,657) = 653058 / 1
LCM(994,657) = 653058
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 537,705?
The HCF of 537,705 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 537/994, 705/657?
Answer: GCF of Numerators as per given numbers 537/994, 705/657 is
GCF of Numerators i.e. for 537,705 is 3
LCM of denominators i.e. for 994,657 is 653058.
Thus, GCF of Fractions is 3/653058.Finally, GCF of Fractions for 537/994, 705/657 is 3/653058.