Use our free GCF of Fractions Calculator tool to compute the GCF of 832/405, 972/720 i.e 4/6480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/405, 972/720.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 832/405,972/720
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 832/405,972/720, numerators are 832,972
Denominators are 405,720
The GCF of 832,972 is 4 .
LCM of 405,720 is 6480.
The greatest common factor of 832/405,972/720 = [GCF of 832,972]/[LCM of 405,720]= 4/6480
Therefore, the GCF of 832/405,972/720 is 4/6480.
To find the highest common factor of 832,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 832,972 is 4.
Lets's calculate GCF of 832,972
2 | 832, 972 |
2 | 416, 486 |
208, 243 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
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
Greatest Common Factor
We found the factors 832,972 . The biggest common factor number is the GCF number.
So the greatest common factor 832,972 is 4.
Lets's calculate LCM of 405,720
3 | 405, 720 |
3 | 135, 240 |
5 | 45, 80 |
9, 16 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 9 x 16 = 6480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/6480
Therefore, the GCF of Fractions 832/405,972/720 is 4/6480
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 405,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,720) = 45
common factors(in case of two or more numbers have common factors) = 1
GCF(405,720) x common factors =45 x 1 = 45
LCM(405,720) = ( 405 × 720 ) / 45
LCM(405,720) = 291600 / 45
LCM(405,720) = 6480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 832,972?
The HCF of 832,972 is 4
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 832/405, 972/720?
Answer: GCF of Numerators as per given numbers 832/405, 972/720 is
GCF of Numerators i.e. for 832,972 is 4
LCM of denominators i.e. for 405,720 is 6480.
Thus, GCF of Fractions is 4/6480.Finally, GCF of Fractions for 832/405, 972/720 is 4/6480.