Proper divisors: Difference between revisions

=={{header|Algol-M}}==

Algol-M's maximum allowed integer value of 16,383 prevented searching up to 20,000 for the number with the most divisors, so the code here searches only up to 10,000.

<lang algol>

BEGIN

% COMPUTE P MOD Q %

INTEGER FUNCTION MOD (P, Q);

INTEGER P, Q;

BEGIN

MOD := P - Q * (P / Q);

END;

% COUNT, AND OPTIONALLY DISPLAY, PROPER DIVISORS OF N %

INTEGER FUNCTION DIVISORS(N, DISPLAY);

INTEGER N, DISPLAY;

BEGIN

INTEGER I, LIMIT, COUNT, START, DELTA;

IF MOD(N, 2) = 0 THEN

BEGIN

START := 2;

DELTA := 1;

END

ELSE % ONLY NEED TO CHECK ODD DIVISORS %

BEGIN

START := 3;

DELTA := 2;

END;

% 1 IS ALWAYS A DIVISOR %

COUNT := 1;

% ANY NON-ZERO VALUE FOR DISPLAY IS TRUE %

IF DISPLAY <> 0 THEN WRITEON(1);

% CHECK REMAINING POTENTIAL DIVISORS %

I := START;

LIMIT := N / START;

WHILE I <= LIMIT DO

BEGIN

IF MOD(N, I) = 0 THEN

BEGIN

IF DISPLAY <> 0 THEN WRITEON(I);

COUNT := COUNT + 1;

END;

I := I + DELTA;

IF COUNT = 1 THEN LIMIT := N / I;

END;

DIVISORS := COUNT;

END;

COMMENT MAIN PROGRAM BEGINS HERE;

INTEGER I, NDIV, TRUE, FALSE, HIGHDIV, HIGHNUM;

TRUE := -1;

FALSE := 0;

WRITE("PROPER DIVISORS OF FIRST TEN NUMBERS:");

FOR I := 1 STEP 1 UNTIL 10 DO

BEGIN

WRITE(I, " : ");

NDIV := DIVISORS(I, TRUE);

END;

WRITE("SEARCHING FOR NUMBER WITH MOST DIVISORS ...");

HIGHDIV := 1;

HIGHNUM := 1;

FOR I := 1 STEP 1 UNTIL 10000 DO

BEGIN

NDIV := DIVISORS(I, FALSE);

IF NDIV > HIGHDIV THEN

BEGIN

HIGHDIV := NDIV;

HIGHNUM := I;

END;

END;

WRITE("THE NUMBER IS:", HIGHNUM);

WRITE("IT HAS", HIGHDIV, " DIVISORS");

END

</lang>

{{out}}

<pre>

PROPER DIVISORS OF FIRST TEN NUMBERS:

1 : 1

2 : 1

3 : 1

4 : 1 2

5 : 1

6 : 1 2 3

7 : 1

8 : 1 2 4

9 : 1 3

10 : 1 2 5

SEARCHING FOR NUMBER WITH MOST DIVISORS:

THE NUMBER IS: 7560

IT HAS 63 DIVISORS

</pre>