# how to calculate modulus in matlab ?

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ahmed on 15 May 2013
Edited: James Tursa on 31 May 2023
Hi everyone,
the question seems simple as using mod works for small numbers not for large numbers.
i want to calculate mod( (4^15)*(21^13),47) the matlab ans= 21 but the correct ans = 3 using the windows calculator. is there any way in matlab to calculate such modulus ?

James Tursa on 17 May 2013
See this newsgroup thread where Bruno Luong gives advice on how to do this calculation without using the symbolic toolbox:

Roger Stafford on 15 May 2013
The number you describe is far too large for accurate numerical computation using only 'double' floating points numbers. However, the 'mod' function also works with symbolic numbers using the symbolic toolbox. You can compute with these to any accuracy you wish.

Walter Roberson on 15 May 2013
Roger Stafford on 16 May 2013
The number 21^13 as computed with 'double' is too large to be computed exactly. Its least five bits must necessarily be rounded to zeros to fit within 53 bits and consequently it gives:
mod(21^13,47) = 2,
whereas the true modulo 47 value is:
mod(mod(21^7,47)*mod(21^6,47),47) = 7.

ahmed on 17 May 2013
Thanks for your help any way , but even the powermod function or any of the above functions in url links can calculate the correct answer which is 3 .
trying:
powermod( (4^15) * (21^13) , 1 , 47 ) gives 21 but the correct ans using windows calculator is 3 and it is equivelant to the answer in my cryptography study book .
Walter Roberson on 17 May 2013
Edited: James Tursa on 31 May 2023
mod(powermod(4, 15, 47) * powermod(21, 13, 47), 47)
ans = 3