GCF of 820/13, 410/133
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 820/13, 410/133 i.e 410/1729 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/13, 410/133.
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 820/13,410/133?
Given fractions are 820/13,410/133
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 820/13,410/133, numerators are 820,410
Denominators are 13,133
The GCF of 820,410 is 410 .
LCM of 13,133 is 1729.
The greatest common factor of 820/13,410/133 = [GCF of 820,410]/[LCM of 13,133]= 410/1729
Therefore, the GCF of 820/13,410/133 is 410/1729.
To find the highest common factor of 820,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 820,410 is 410.
Lets's calculate GCF of 820,410
| 2 | 820, 410 |
| 5 | 410, 205 |
| 41 | 82, 41 |
| 2, 1 |
∴ So the GCF of the given numbers is 2 x 5 x 41 = 410
Greatest Common Factor of 820,410 By Matching Biggest Common Factor Method
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 820,410 . The biggest common factor number is the GCF number.
So the greatest common factor 820,410 is 410.
Lets's calculate LCM of 13,133
Given numbers has no common factors except 1. So, there LCM is their product i.e 1729
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 410/1729
Therefore, the GCF of Fractions 820/13,410/133 is 410/1729
Least Common Multiple of 13,133 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 13,133 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,133) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,133) x common factors =1 x 1 = 1
LCM(13,133) = ( 13 × 133 ) / 1
LCM(13,133) = 1729 / 1
LCM(13,133) = 1729
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FAQs on GCF of Fractions of 820/13, 410/133
1. What is the HCF of 820,410?
The HCF of 820,410 is 410
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 820/13, 410/133?
Answer: GCF of Numerators as per given numbers 820/13, 410/133 is
GCF of Numerators i.e. for 820,410 is 410
LCM of denominators i.e. for 13,133 is 1729.
Thus, GCF of Fractions is 410/1729.Finally, GCF of Fractions for 820/13, 410/133 is 410/1729.