GCF of 5729/862, 7650/286
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5729/862, 7650/286 i.e 17/123266 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5729/862, 7650/286.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 5729/862,7650/286?
Given fractions are 5729/862,7650/286
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 5729/862,7650/286, numerators are 5729,7650
Denominators are 862,286
The GCF of 5729,7650 is 17 .
LCM of 862,286 is 123266.
The greatest common factor of 5729/862,7650/286 = [GCF of 5729,7650]/[LCM of 862,286]= 17/123266
Therefore, the GCF of 5729/862,7650/286 is 17/123266.
To find the highest common factor of 5729,7650, we have to find the factors of both numbers and list the highest common factor.
The factors of 5729 are 1, 17, 337, 5729
The factors of 7650 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 25, 30, 34, 45, 50, 51, 75, 85, 90, 102, 150, 153, 170, 225, 255, 306, 425, 450, 510, 765, 850, 1275, 1530, 2550, 3825, 7650
The HCF of 5729,7650 is 17.
Lets's calculate GCF of 5729,7650
| 17 | 5729, 7650 |
| 337, 450 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 5729,7650 By Matching Biggest Common Factor Method
Now, list down the factors of 5729
:1,17,337,5729
Now, list down the factors of 7650
:1,2,3,5,6,9,10,15,17,18,25,30,34,45,50,51,75,85,90,102,150,153,170,225,255,306,425,450,510,765,850,1275,1530,2550,3825,7650
Greatest Common Factor
We found the factors 5729,7650 . The biggest common factor number is the GCF number.
So the greatest common factor 5729,7650 is 17.
Lets's calculate LCM of 862,286
| 2 | 862, 286 |
| 431, 143 |
∴ So the LCM of the given numbers is 2 x 431 x 143 = 123266
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/123266
Therefore, the GCF of Fractions 5729/862,7650/286 is 17/123266
Least Common Multiple of 862,286 with GCF Formula
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 862,286 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(862,286) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(862,286) x common factors =2 x 1 = 2
LCM(862,286) = ( 862 × 286 ) / 2
LCM(862,286) = 246532 / 2
LCM(862,286) = 123266
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 5729/862, 7650/286
1. What is the HCF of 5729,7650?
The HCF of 5729,7650 is 17
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 5729/862, 7650/286?
Answer: GCF of Numerators as per given numbers 5729/862, 7650/286 is
GCF of Numerators i.e. for 5729,7650 is 17
LCM of denominators i.e. for 862,286 is 123266.
Thus, GCF of Fractions is 17/123266.Finally, GCF of Fractions for 5729/862, 7650/286 is 17/123266.