Use our free GCF of Fractions Calculator tool to compute the GCF of 769/728, 617/282 i.e 1/102648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 769/728, 617/282.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 769/728,617/282
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 769/728,617/282, numerators are 769,617
Denominators are 728,282
The GCF of 769,617 is 1 .
LCM of 728,282 is 102648.
The greatest common factor of 769/728,617/282 = [GCF of 769,617]/[LCM of 728,282]= 1/102648
Therefore, the GCF of 769/728,617/282 is 1/102648.
To find the highest common factor of 769,617, we have to find the factors of both numbers and list the highest common factor.
The factors of 769 are 1, 769
The factors of 617 are 1, 617
The HCF of 769,617 is 1.
Lets's calculate GCF of 769,617
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 769
:1,769
Now, list down the factors of 617
:1,617
Greatest Common Factor
We found the factors 769,617 . The biggest common factor number is the GCF number.
So the greatest common factor 769,617 is 1.
Lets's calculate LCM of 728,282
2 | 728, 282 |
364, 141 |
∴ So the LCM of the given numbers is 2 x 364 x 141 = 102648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102648
Therefore, the GCF of Fractions 769/728,617/282 is 1/102648
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 728,282 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,282) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(728,282) x common factors =2 x 1 = 2
LCM(728,282) = ( 728 × 282 ) / 2
LCM(728,282) = 205296 / 2
LCM(728,282) = 102648
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 769,617?
The HCF of 769,617 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 769/728, 617/282?
Answer: GCF of Numerators as per given numbers 769/728, 617/282 is
GCF of Numerators i.e. for 769,617 is 1
LCM of denominators i.e. for 728,282 is 102648.
Thus, GCF of Fractions is 1/102648.Finally, GCF of Fractions for 769/728, 617/282 is 1/102648.