Use our free GCF of Fractions Calculator tool to compute the GCF of 829/72, 136/44, 317/21 i.e 1/5544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/72, 136/44, 317/21.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 829/72,136/44,317/21
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 829/72,136/44,317/21, numerators are 829,136,317
Denominators are 72,44,21
The GCF of 829,136,317 is 1 .
LCM of 72,44,21 is 5544.
The greatest common factor of 829/72,136/44,317/21 = [GCF of 829,136,317]/[LCM of 72,44,21]= 1/5544
Therefore, the GCF of 829/72,136/44,317/21 is 1/5544.
To find the highest common factor of 829,136,317, we have to find the factors of both numbers and list the highest common factor.
The factors of 829 are 1, 829
The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136
The factors of 317 are 1, 317
The HCF of 829,136,317 is 1.
Lets's calculate GCF of 829,136,317
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 829
:1,829
Now, list down the factors of 136
:1,2,4,8,17,34,68,136
Now, list down the factors of 317
:1,317
Greatest Common Factor
We found the factors 829,136,317 . The biggest common factor number is the GCF number.
So the greatest common factor 829,136,317 is 1.
Lets's calculate LCM of 72,44,21
2 | 72, 44, 21 |
2 | 36, 22, 21 |
3 | 18, 11, 21 |
6, 11, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 6 x 11 x 7 = 5544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5544
Therefore, the GCF of Fractions 829/72,136/44,317/21 is 1/5544
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 72,44,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,44,21) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(72,44,21) x common factors =1 x 12 = 12
LCM(72,44,21) = ( 72 × 44 × 21 ) / 12
LCM(72,44,21) = 66528 / 12
LCM(72,44,21) = 5544
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 829,136,317?
The HCF of 829,136,317 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 829/72, 136/44, 317/21?
Answer: GCF of Numerators as per given numbers 829/72, 136/44, 317/21 is
GCF of Numerators i.e. for 829,136,317 is 1
LCM of denominators i.e. for 72,44,21 is 5544.
Thus, GCF of Fractions is 1/5544.Finally, GCF of Fractions for 829/72, 136/44, 317/21 is 1/5544.