GCF of 8014/413, 8424/789
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8014/413, 8424/789 i.e 2/325857 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8014/413, 8424/789.
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 8014/413,8424/789?
Given fractions are 8014/413,8424/789
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 8014/413,8424/789, numerators are 8014,8424
Denominators are 413,789
The GCF of 8014,8424 is 2 .
LCM of 413,789 is 325857.
The greatest common factor of 8014/413,8424/789 = [GCF of 8014,8424]/[LCM of 413,789]= 2/325857
Therefore, the GCF of 8014/413,8424/789 is 2/325857.
To find the highest common factor of 8014,8424, we have to find the factors of both numbers and list the highest common factor.
The factors of 8014 are 1, 2, 4007, 8014
The factors of 8424 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 81, 104, 108, 117, 156, 162, 216, 234, 312, 324, 351, 468, 648, 702, 936, 1053, 1404, 2106, 2808, 4212, 8424
The HCF of 8014,8424 is 2.
Lets's calculate GCF of 8014,8424
| 2 | 8014, 8424 |
| 4007, 4212 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8014,8424 By Matching Biggest Common Factor Method
Now, list down the factors of 8014
:1,2,4007,8014
Now, list down the factors of 8424
:1,2,3,4,6,8,9,12,13,18,24,26,27,36,39,52,54,72,78,81,104,108,117,156,162,216,234,312,324,351,468,648,702,936,1053,1404,2106,2808,4212,8424
Greatest Common Factor
We found the factors 8014,8424 . The biggest common factor number is the GCF number.
So the greatest common factor 8014,8424 is 2.
Lets's calculate LCM of 413,789
Given numbers has no common factors except 1. So, there LCM is their product i.e 325857
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/325857
Therefore, the GCF of Fractions 8014/413,8424/789 is 2/325857
Least Common Multiple of 413,789 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 413,789 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,789) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,789) x common factors =1 x 1 = 1
LCM(413,789) = ( 413 × 789 ) / 1
LCM(413,789) = 325857 / 1
LCM(413,789) = 325857
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FAQs on GCF of Fractions of 8014/413, 8424/789
1. What is the HCF of 8014,8424?
The HCF of 8014,8424 is 2
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 8014/413, 8424/789?
Answer: GCF of Numerators as per given numbers 8014/413, 8424/789 is
GCF of Numerators i.e. for 8014,8424 is 2
LCM of denominators i.e. for 413,789 is 325857.
Thus, GCF of Fractions is 2/325857.Finally, GCF of Fractions for 8014/413, 8424/789 is 2/325857.