# Factorial using a for loop

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Joseph am 14 Apr. 2023
Kommentiert: John D'Errico am 14 Apr. 2023
I need to write a for loop that calculates the factorial 100
This is the code that I have written. I now need to display the value of 100! and asign it to the variable nf
How could I go about that?
n=100
x=1
for b=1:n
x=x*b
end
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### Antworten (2)

Walter Roberson am 14 Apr. 2023
Bearbeitet: Walter Roberson am 14 Apr. 2023
n=75;
x=sym(1);
for b=1:n
x=x*b;
end
nf_sym = x
nf_sym =
24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000
You will not be able to calculate this accurately using double precision.
format long g
n=75;
x=(1);
for b=1:n
x=x*b;
end
nf = x
nf =
2.48091408113954e+109
double(nf_sym) - nf
ans =
8.34369935906606e+93
That is, the final digits in the pure double precision calculation are not correct compared to calculating exactly and taking double precision afterwards.
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Les Beckham am 14 Apr. 2023
Your code works fine (though I would add semicolons to the end of all lines except the for and end to avoid spewing a bunch of stuff to the command window).
Then add this after your existing code to "assign it to the variable nf". Or, you could just replace the x variable with nf.
nf = x
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John D'Errico am 14 Apr. 2023
All correct. I would add however, that factorial(100) is NOT representable exactly as a double precision number.
factorial(100)
ans = 9.3326e+157
So only the first 16 decimal digits of that result will be correct.

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