GCF of 829/84, 309/268
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 829/84, 309/268 i.e 1/5628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/84, 309/268.
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 829/84,309/268?
Given fractions are 829/84,309/268
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 829/84,309/268, numerators are 829,309
Denominators are 84,268
The GCF of 829,309 is 1 .
LCM of 84,268 is 5628.
The greatest common factor of 829/84,309/268 = [GCF of 829,309]/[LCM of 84,268]= 1/5628
Therefore, the GCF of 829/84,309/268 is 1/5628.
To find the highest common factor of 829,309, 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 309 are 1, 3, 103, 309
The HCF of 829,309 is 1.
Lets's calculate GCF of 829,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 829,309 By Matching Biggest Common Factor Method
Now, list down the factors of 829
:1,829
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 829,309 . The biggest common factor number is the GCF number.
So the greatest common factor 829,309 is 1.
Lets's calculate LCM of 84,268
| 2 | 84, 268 |
| 2 | 42, 134 |
| 21, 67 |
∴ So the LCM of the given numbers is 2 x 2 x 21 x 67 = 5628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5628
Therefore, the GCF of Fractions 829/84,309/268 is 1/5628
Least Common Multiple of 84,268 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 84,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,268) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(84,268) x common factors =4 x 1 = 4
LCM(84,268) = ( 84 × 268 ) / 4
LCM(84,268) = 22512 / 4
LCM(84,268) = 5628
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FAQs on GCF of Fractions of 829/84, 309/268
1. What is the HCF of 829,309?
The HCF of 829,309 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 829/84, 309/268?
Answer: GCF of Numerators as per given numbers 829/84, 309/268 is
GCF of Numerators i.e. for 829,309 is 1
LCM of denominators i.e. for 84,268 is 5628.
Thus, GCF of Fractions is 1/5628.Finally, GCF of Fractions for 829/84, 309/268 is 1/5628.