Use our free GCF of Fractions Calculator tool to compute the GCF of 56/65, 13/166, 540/498 i.e 1/32370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/65, 13/166, 540/498.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 56/65,13/166,540/498
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 56/65,13/166,540/498, numerators are 56,13,540
Denominators are 65,166,498
The GCF of 56,13,540 is 1 .
LCM of 65,166,498 is 32370.
The greatest common factor of 56/65,13/166,540/498 = [GCF of 56,13,540]/[LCM of 65,166,498]= 1/32370
Therefore, the GCF of 56/65,13/166,540/498 is 1/32370.
To find the highest common factor of 56,13,540, we have to find the factors of both numbers and list the highest common factor.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 13 are 1, 13
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The HCF of 56,13,540 is 1.
Lets's calculate GCF of 56,13,540
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 13
:1,13
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Greatest Common Factor
We found the factors 56,13,540 . The biggest common factor number is the GCF number.
So the greatest common factor 56,13,540 is 1.
Lets's calculate LCM of 65,166,498
2 | 65, 166, 498 |
83 | 65, 83, 249 |
65, 1, 3 |
∴ So the LCM of the given numbers is 2 x 83 x 65 x 1 x 3 = 32370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32370
Therefore, the GCF of Fractions 56/65,13/166,540/498 is 1/32370
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 65,166,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,166,498) = 1
common factors(in case of two or more numbers have common factors) = 166
GCF(65,166,498) x common factors =1 x 166 = 166
LCM(65,166,498) = ( 65 × 166 × 498 ) / 166
LCM(65,166,498) = 5373420 / 166
LCM(65,166,498) = 32370
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 56,13,540?
The HCF of 56,13,540 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 56/65, 13/166, 540/498?
Answer: GCF of Numerators as per given numbers 56/65, 13/166, 540/498 is
GCF of Numerators i.e. for 56,13,540 is 1
LCM of denominators i.e. for 65,166,498 is 32370.
Thus, GCF of Fractions is 1/32370.Finally, GCF of Fractions for 56/65, 13/166, 540/498 is 1/32370.