GCF of 728/146, 8229/702
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 728/146, 8229/702 i.e 13/51246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/146, 8229/702.
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 728/146,8229/702?
Given fractions are 728/146,8229/702
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 728/146,8229/702, numerators are 728,8229
Denominators are 146,702
The GCF of 728,8229 is 13 .
LCM of 146,702 is 51246.
The greatest common factor of 728/146,8229/702 = [GCF of 728,8229]/[LCM of 146,702]= 13/51246
Therefore, the GCF of 728/146,8229/702 is 13/51246.
To find the highest common factor of 728,8229, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 8229 are 1, 3, 13, 39, 211, 633, 2743, 8229
The HCF of 728,8229 is 13.
Lets's calculate GCF of 728,8229
| 13 | 728, 8229 |
| 56, 633 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 728,8229 By Matching Biggest Common Factor Method
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 8229
:1,3,13,39,211,633,2743,8229
Greatest Common Factor
We found the factors 728,8229 . The biggest common factor number is the GCF number.
So the greatest common factor 728,8229 is 13.
Lets's calculate LCM of 146,702
| 2 | 146, 702 |
| 73, 351 |
∴ So the LCM of the given numbers is 2 x 73 x 351 = 51246
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/51246
Therefore, the GCF of Fractions 728/146,8229/702 is 13/51246
Least Common Multiple of 146,702 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 146,702 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(146,702) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(146,702) x common factors =2 x 1 = 2
LCM(146,702) = ( 146 × 702 ) / 2
LCM(146,702) = 102492 / 2
LCM(146,702) = 51246
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FAQs on GCF of Fractions of 728/146, 8229/702
1. What is the HCF of 728,8229?
The HCF of 728,8229 is 13
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 728/146, 8229/702?
Answer: GCF of Numerators as per given numbers 728/146, 8229/702 is
GCF of Numerators i.e. for 728,8229 is 13
LCM of denominators i.e. for 146,702 is 51246.
Thus, GCF of Fractions is 13/51246.Finally, GCF of Fractions for 728/146, 8229/702 is 13/51246.