Number theory in CALCULA
The Number theory field works on integers: divisibility, primes, congruences. Results are exact, with no rounding.
GCD, LCM and prime factors
The GCD (greatest common divisor) comes from Euclid's algorithm: replace the larger number by its remainder in the division by the smaller one, until the remainder is zero. Every integer > 1 factors uniquely into primes.
Example
60 = 2²·3·5 and 84 = 2²·3·7. Their GCD is 2²·3 = 12, their LCM is 2²·3·5·7 = 420. Check: 12 × 420 = 5040 = 60 × 84.
Modular arithmetic
Working “modulo n” means keeping only the remainder of the division by n — the arithmetic of the clock (13:00 ≡ 1:00, mod 12). It sits at the heart of cryptography and of checksums.
Example
Which weekday in 100 days? 100 mod 7 = 2: move forward two days. Fermat's little theorem and modular exponentiation, used in RSA, are also computed in CALCULA.
Typing it into CALCULA
“≡” menu → number theory: enter the integers, choose the operation (GCD, LCM, factorisation, primality test, modular power, modular inverse). See also conversions for number bases.