Use our free GCF of Fractions Calculator tool to compute the GCF of 972/260, 531/164 i.e 9/10660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/260, 531/164.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 972/260,531/164
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 972/260,531/164, numerators are 972,531
Denominators are 260,164
The GCF of 972,531 is 9 .
LCM of 260,164 is 10660.
The greatest common factor of 972/260,531/164 = [GCF of 972,531]/[LCM of 260,164]= 9/10660
Therefore, the GCF of 972/260,531/164 is 9/10660.
To find the highest common factor of 972,531, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 531 are 1, 3, 9, 59, 177, 531
The HCF of 972,531 is 9.
Lets's calculate GCF of 972,531
3 | 972, 531 |
3 | 324, 177 |
108, 59 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 531
:1,3,9,59,177,531
Greatest Common Factor
We found the factors 972,531 . The biggest common factor number is the GCF number.
So the greatest common factor 972,531 is 9.
Lets's calculate LCM of 260,164
2 | 260, 164 |
2 | 130, 82 |
65, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 65 x 41 = 10660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/10660
Therefore, the GCF of Fractions 972/260,531/164 is 9/10660
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 260,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,164) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(260,164) x common factors =4 x 1 = 4
LCM(260,164) = ( 260 × 164 ) / 4
LCM(260,164) = 42640 / 4
LCM(260,164) = 10660
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 972,531?
The HCF of 972,531 is 9
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 972/260, 531/164?
Answer: GCF of Numerators as per given numbers 972/260, 531/164 is
GCF of Numerators i.e. for 972,531 is 9
LCM of denominators i.e. for 260,164 is 10660.
Thus, GCF of Fractions is 9/10660.Finally, GCF of Fractions for 972/260, 531/164 is 9/10660.