GCF of 825/299, 3678/857
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 825/299, 3678/857 i.e 3/256243 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/299, 3678/857.
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 825/299,3678/857?
Given fractions are 825/299,3678/857
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 825/299,3678/857, numerators are 825,3678
Denominators are 299,857
The GCF of 825,3678 is 3 .
LCM of 299,857 is 256243.
The greatest common factor of 825/299,3678/857 = [GCF of 825,3678]/[LCM of 299,857]= 3/256243
Therefore, the GCF of 825/299,3678/857 is 3/256243.
To find the highest common factor of 825,3678, we have to find the factors of both numbers and list the highest common factor.
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678
The HCF of 825,3678 is 3.
Lets's calculate GCF of 825,3678
| 3 | 825, 3678 |
| 275, 1226 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 825,3678 By Matching Biggest Common Factor Method
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Now, list down the factors of 3678
:1,2,3,6,613,1226,1839,3678
Greatest Common Factor
We found the factors 825,3678 . The biggest common factor number is the GCF number.
So the greatest common factor 825,3678 is 3.
Lets's calculate LCM of 299,857
Given numbers has no common factors except 1. So, there LCM is their product i.e 256243
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/256243
Therefore, the GCF of Fractions 825/299,3678/857 is 3/256243
Least Common Multiple of 299,857 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 299,857 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(299,857) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(299,857) x common factors =1 x 1 = 1
LCM(299,857) = ( 299 × 857 ) / 1
LCM(299,857) = 256243 / 1
LCM(299,857) = 256243
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FAQs on GCF of Fractions of 825/299, 3678/857
1. What is the HCF of 825,3678?
The HCF of 825,3678 is 3
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 825/299, 3678/857?
Answer: GCF of Numerators as per given numbers 825/299, 3678/857 is
GCF of Numerators i.e. for 825,3678 is 3
LCM of denominators i.e. for 299,857 is 256243.
Thus, GCF of Fractions is 3/256243.Finally, GCF of Fractions for 825/299, 3678/857 is 3/256243.