GCF of 8157/417, 8364/1982
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8157/417, 8364/1982 i.e 3/826494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8157/417, 8364/1982.
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 8157/417,8364/1982?
Given fractions are 8157/417,8364/1982
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 8157/417,8364/1982, numerators are 8157,8364
Denominators are 417,1982
The GCF of 8157,8364 is 3 .
LCM of 417,1982 is 826494.
The greatest common factor of 8157/417,8364/1982 = [GCF of 8157,8364]/[LCM of 417,1982]= 3/826494
Therefore, the GCF of 8157/417,8364/1982 is 3/826494.
To find the highest common factor of 8157,8364, we have to find the factors of both numbers and list the highest common factor.
The factors of 8157 are 1, 3, 2719, 8157
The factors of 8364 are 1, 2, 3, 4, 6, 12, 17, 34, 41, 51, 68, 82, 102, 123, 164, 204, 246, 492, 697, 1394, 2091, 2788, 4182, 8364
The HCF of 8157,8364 is 3.
Lets's calculate GCF of 8157,8364
| 3 | 8157, 8364 |
| 2719, 2788 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8157,8364 By Matching Biggest Common Factor Method
Now, list down the factors of 8157
:1,3,2719,8157
Now, list down the factors of 8364
:1,2,3,4,6,12,17,34,41,51,68,82,102,123,164,204,246,492,697,1394,2091,2788,4182,8364
Greatest Common Factor
We found the factors 8157,8364 . The biggest common factor number is the GCF number.
So the greatest common factor 8157,8364 is 3.
Lets's calculate LCM of 417,1982
Given numbers has no common factors except 1. So, there LCM is their product i.e 826494
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/826494
Therefore, the GCF of Fractions 8157/417,8364/1982 is 3/826494
Least Common Multiple of 417,1982 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 417,1982 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(417,1982) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(417,1982) x common factors =1 x 1 = 1
LCM(417,1982) = ( 417 × 1982 ) / 1
LCM(417,1982) = 826494 / 1
LCM(417,1982) = 826494
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FAQs on GCF of Fractions of 8157/417, 8364/1982
1. What is the HCF of 8157,8364?
The HCF of 8157,8364 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 8157/417, 8364/1982?
Answer: GCF of Numerators as per given numbers 8157/417, 8364/1982 is
GCF of Numerators i.e. for 8157,8364 is 3
LCM of denominators i.e. for 417,1982 is 826494.
Thus, GCF of Fractions is 3/826494.Finally, GCF of Fractions for 8157/417, 8364/1982 is 3/826494.