Use our free GCF of Fractions Calculator tool to compute the GCF of 537/462, 716/561 i.e 179/7854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 537/462, 716/561.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 537/462,716/561
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 537/462,716/561, numerators are 537,716
Denominators are 462,561
The GCF of 537,716 is 179 .
LCM of 462,561 is 7854.
The greatest common factor of 537/462,716/561 = [GCF of 537,716]/[LCM of 462,561]= 179/7854
Therefore, the GCF of 537/462,716/561 is 179/7854.
To find the highest common factor of 537,716, 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 716 are 1, 2, 4, 179, 358, 716
The HCF of 537,716 is 179.
Lets's calculate GCF of 537,716
179 | 537, 716 |
3, 4 |
∴ So the GCF of the given numbers is 179 = 179
Now, list down the factors of 537
:1,3,179,537
Now, list down the factors of 716
:1,2,4,179,358,716
Greatest Common Factor
We found the factors 537,716 . The biggest common factor number is the GCF number.
So the greatest common factor 537,716 is 179.
Lets's calculate LCM of 462,561
3 | 462, 561 |
11 | 154, 187 |
14, 17 |
∴ So the LCM of the given numbers is 3 x 11 x 14 x 17 = 7854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 179/7854
Therefore, the GCF of Fractions 537/462,716/561 is 179/7854
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 462,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,561) = 33
common factors(in case of two or more numbers have common factors) = 1
GCF(462,561) x common factors =33 x 1 = 33
LCM(462,561) = ( 462 × 561 ) / 33
LCM(462,561) = 259182 / 33
LCM(462,561) = 7854
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 537,716?
The HCF of 537,716 is 179
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 537/462, 716/561?
Answer: GCF of Numerators as per given numbers 537/462, 716/561 is
GCF of Numerators i.e. for 537,716 is 179
LCM of denominators i.e. for 462,561 is 7854.
Thus, GCF of Fractions is 179/7854.Finally, GCF of Fractions for 537/462, 716/561 is 179/7854.