GCF of 7413/417, 3864/6914
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7413/417, 3864/6914 i.e 21/2883138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7413/417, 3864/6914.
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 7413/417,3864/6914?
Given fractions are 7413/417,3864/6914
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 7413/417,3864/6914, numerators are 7413,3864
Denominators are 417,6914
The GCF of 7413,3864 is 21 .
LCM of 417,6914 is 2883138.
The greatest common factor of 7413/417,3864/6914 = [GCF of 7413,3864]/[LCM of 417,6914]= 21/2883138
Therefore, the GCF of 7413/417,3864/6914 is 21/2883138.
To find the highest common factor of 7413,3864, we have to find the factors of both numbers and list the highest common factor.
The factors of 7413 are 1, 3, 7, 21, 353, 1059, 2471, 7413
The factors of 3864 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 56, 69, 84, 92, 138, 161, 168, 184, 276, 322, 483, 552, 644, 966, 1288, 1932, 3864
The HCF of 7413,3864 is 21.
Lets's calculate GCF of 7413,3864
| 3 | 7413, 3864 |
| 7 | 2471, 1288 |
| 353, 184 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 7413,3864 By Matching Biggest Common Factor Method
Now, list down the factors of 7413
:1,3,7,21,353,1059,2471,7413
Now, list down the factors of 3864
:1,2,3,4,6,7,8,12,14,21,23,24,28,42,46,56,69,84,92,138,161,168,184,276,322,483,552,644,966,1288,1932,3864
Greatest Common Factor
We found the factors 7413,3864 . The biggest common factor number is the GCF number.
So the greatest common factor 7413,3864 is 21.
Lets's calculate LCM of 417,6914
Given numbers has no common factors except 1. So, there LCM is their product i.e 2883138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/2883138
Therefore, the GCF of Fractions 7413/417,3864/6914 is 21/2883138
Least Common Multiple of 417,6914 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 417,6914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(417,6914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(417,6914) x common factors =1 x 1 = 1
LCM(417,6914) = ( 417 × 6914 ) / 1
LCM(417,6914) = 2883138 / 1
LCM(417,6914) = 2883138
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FAQs on GCF of Fractions of 7413/417, 3864/6914
1. What is the HCF of 7413,3864?
The HCF of 7413,3864 is 21
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 7413/417, 3864/6914?
Answer: GCF of Numerators as per given numbers 7413/417, 3864/6914 is
GCF of Numerators i.e. for 7413,3864 is 21
LCM of denominators i.e. for 417,6914 is 2883138.
Thus, GCF of Fractions is 21/2883138.Finally, GCF of Fractions for 7413/417, 3864/6914 is 21/2883138.