Factorizing Numbers

This program factorizes a user-supplied integer into its prime factors, displaying the result in the form “N = 1 X f1 X f2 …”. It uses trial division, starting at 2 and then stepping through odd numbers only (achieved by setting F to 1 after the initial factor of 2 is exhausted, then always adding 2). The square root of the original number is pre-computed and stored in S to limit the search, a classic optimisation for trial division. A flag variable PF tracks whether any factor has been found so that a lone prime can be labelled “PRIME NUMBER”. The program loops back to line 5 (the REM header) after each factorisation, effectively restarting cleanly without a CLS of the REM line itself.

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Program Analysis

Program Structure

The program is organised into four functional blocks, each at a distinct line-number range:

1. Lines 5, 100–120 — title display and user input.
2. Lines 130–250 — initialisation and the inner trial-division loop.
3. Lines 300–340 — factor-advance logic (move to the next candidate divisor).
4. Lines 400–460 — result display, prompt, and restart.

Lines 500–510 are a SAVE/RUN tail used for distribution; they are never reached during normal execution.

Algorithm: Trial Division

The algorithm divides the working copy N repeatedly by the current factor candidate F, printing each factor found. The original value is preserved in NN for the prime-number message and for the special-case guard at line 200.

The divisor sequence is: 2, then all odd numbers from 3 upward. This is achieved by a small trick at line 310: after exhausting the factor 2, F is set to 1 so that the unconditional LET F=F+2 at line 330 brings it to 3, and thereafter always increments by 2, skipping even candidates entirely.

The upper bound is the pre-computed square root S=SQR N (line 150), stored once at the start. This correctly limits the search because if no factor ≤ √N exists, the remaining N must itself be prime.

Key Variables

Variable	Role
N	Working number, divided down as factors are found
NN	Original input, preserved for the prime label
F	Current trial divisor
S	Square root of original N, loop upper bound
PF	Prime flag: 0 = no factor found yet, 1 = composite
A$	Dummy variable to consume the ENTER keypress

Notable Techniques

• Compound condition at line 300: IF PF=0 AND F>S OR N=1 THEN GOTO 400 — on ZX81 BASIC, AND binds more tightly than OR, so this correctly exits when either all factors are exhausted (N=1) or no factor was found within the square-root bound.
• Output format: The print statement at line 170 uses four commas to push the output to the fifth print zone before printing the equation start, giving a centred appearance on the 32-column display.
• Restart via GOTO 5: Jumping back to the REM line (line 5) rather than using RUN preserves the variable A$ and avoids re-initialising the system, but it effectively restarts the program flow cleanly.
• Inverse-video REM title: Line 5 stores the program name “NUMBER FACTORS” in inverse video characters, a common ZX81 convention for self-documenting listings visible in the program editor.

Bugs and Anomalies

• Typo in prompt: Line 110 prints "WHATS YOUR MUMBER" — “MUMBER” instead of “NUMBER”. This is a cosmetic error only.
• Special-case guard for N=2: The condition OR NN=2 in line 200 prevents the loop from treating 2 as composite (since 2/2=1, which would trigger the factor branch incorrectly on the second pass). However, the logic is slightly fragile: it relies on NN holding the original input, which works correctly here because NN is never modified.
• Square root not updated: S is computed from the original N at line 150 and never updated as N is divided down. This is actually correct for the purpose of bounding the search, but it means the loop may run a few extra iterations beyond the mathematically minimal bound after partial factorisation. It does not produce wrong results.
• PF flag reset: PF is reset to 0 at line 160 on each run through the initialisation block, ensuring the prime detection is correct for successive inputs.