GCF of 820/71, 123/6567
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 820/71, 123/6567 i.e 41/466257 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/71, 123/6567.
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 820/71,123/6567?
Given fractions are 820/71,123/6567
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 820/71,123/6567, numerators are 820,123
Denominators are 71,6567
The GCF of 820,123 is 41 .
LCM of 71,6567 is 466257.
The greatest common factor of 820/71,123/6567 = [GCF of 820,123]/[LCM of 71,6567]= 41/466257
Therefore, the GCF of 820/71,123/6567 is 41/466257.
To find the highest common factor of 820,123, 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 123 are 1, 3, 41, 123
The HCF of 820,123 is 41.
Lets's calculate GCF of 820,123
| 41 | 820, 123 |
| 20, 3 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 820,123 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 123
:1,3,41,123
Greatest Common Factor
We found the factors 820,123 . The biggest common factor number is the GCF number.
So the greatest common factor 820,123 is 41.
Lets's calculate LCM of 71,6567
Given numbers has no common factors except 1. So, there LCM is their product i.e 466257
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/466257
Therefore, the GCF of Fractions 820/71,123/6567 is 41/466257
Least Common Multiple of 71,6567 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 71,6567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,6567) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,6567) x common factors =1 x 1 = 1
LCM(71,6567) = ( 71 × 6567 ) / 1
LCM(71,6567) = 466257 / 1
LCM(71,6567) = 466257
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FAQs on GCF of Fractions of 820/71, 123/6567
1. What is the HCF of 820,123?
The HCF of 820,123 is 41
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 820/71, 123/6567?
Answer: GCF of Numerators as per given numbers 820/71, 123/6567 is
GCF of Numerators i.e. for 820,123 is 41
LCM of denominators i.e. for 71,6567 is 466257.
Thus, GCF of Fractions is 41/466257.Finally, GCF of Fractions for 820/71, 123/6567 is 41/466257.