GCF of 823/207, 3872/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 823/207, 3872/414 i.e 1/414 easily. The following is the detailed procedure to determine the greatest common factor of fractions 823/207, 3872/414.
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 823/207,3872/414?
Given fractions are 823/207,3872/414
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 823/207,3872/414, numerators are 823,3872
Denominators are 207,414
The GCF of 823,3872 is 1 .
LCM of 207,414 is 414.
The greatest common factor of 823/207,3872/414 = [GCF of 823,3872]/[LCM of 207,414]= 1/414
Therefore, the GCF of 823/207,3872/414 is 1/414.
To find the highest common factor of 823,3872, we have to find the factors of both numbers and list the highest common factor.
The factors of 823 are 1, 823
The factors of 3872 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 121, 176, 242, 352, 484, 968, 1936, 3872
The HCF of 823,3872 is 1.
Lets's calculate GCF of 823,3872
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 823,3872 By Matching Biggest Common Factor Method
Now, list down the factors of 823
:1,823
Now, list down the factors of 3872
:1,2,4,8,11,16,22,32,44,88,121,176,242,352,484,968,1936,3872
Greatest Common Factor
We found the factors 823,3872 . The biggest common factor number is the GCF number.
So the greatest common factor 823,3872 is 1.
Lets's calculate LCM of 207,414
| 3 | 207, 414 |
| 3 | 69, 138 |
| 23 | 23, 46 |
| 1, 2 |
∴ So the LCM of the given numbers is 3 x 3 x 23 x 1 x 2 = 414
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/414
Therefore, the GCF of Fractions 823/207,3872/414 is 1/414
Least Common Multiple of 207,414 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 207,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(207,414) = 207
common factors(in case of two or more numbers have common factors) = 1
GCF(207,414) x common factors =207 x 1 = 207
LCM(207,414) = ( 207 × 414 ) / 207
LCM(207,414) = 85698 / 207
LCM(207,414) = 414
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FAQs on GCF of Fractions of 823/207, 3872/414
1. What is the HCF of 823,3872?
The HCF of 823,3872 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 823/207, 3872/414?
Answer: GCF of Numerators as per given numbers 823/207, 3872/414 is
GCF of Numerators i.e. for 823,3872 is 1
LCM of denominators i.e. for 207,414 is 414.
Thus, GCF of Fractions is 1/414.Finally, GCF of Fractions for 823/207, 3872/414 is 1/414.