GCF of 828/577, 2806/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 828/577, 2806/706 i.e 46/407362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/577, 2806/706.
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 828/577,2806/706?
Given fractions are 828/577,2806/706
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 828/577,2806/706, numerators are 828,2806
Denominators are 577,706
The GCF of 828,2806 is 46 .
LCM of 577,706 is 407362.
The greatest common factor of 828/577,2806/706 = [GCF of 828,2806]/[LCM of 577,706]= 46/407362
Therefore, the GCF of 828/577,2806/706 is 46/407362.
To find the highest common factor of 828,2806, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 2806 are 1, 2, 23, 46, 61, 122, 1403, 2806
The HCF of 828,2806 is 46.
Lets's calculate GCF of 828,2806
| 2 | 828, 2806 |
| 23 | 414, 1403 |
| 18, 61 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 828,2806 By Matching Biggest Common Factor Method
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 2806
:1,2,23,46,61,122,1403,2806
Greatest Common Factor
We found the factors 828,2806 . The biggest common factor number is the GCF number.
So the greatest common factor 828,2806 is 46.
Lets's calculate LCM of 577,706
Given numbers has no common factors except 1. So, there LCM is their product i.e 407362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/407362
Therefore, the GCF of Fractions 828/577,2806/706 is 46/407362
Least Common Multiple of 577,706 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 577,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(577,706) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(577,706) x common factors =1 x 1 = 1
LCM(577,706) = ( 577 × 706 ) / 1
LCM(577,706) = 407362 / 1
LCM(577,706) = 407362
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FAQs on GCF of Fractions of 828/577, 2806/706
1. What is the HCF of 828,2806?
The HCF of 828,2806 is 46
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 828/577, 2806/706?
Answer: GCF of Numerators as per given numbers 828/577, 2806/706 is
GCF of Numerators i.e. for 828,2806 is 46
LCM of denominators i.e. for 577,706 is 407362.
Thus, GCF of Fractions is 46/407362.Finally, GCF of Fractions for 828/577, 2806/706 is 46/407362.