MOD
From QB64 Wiki
MOD is mathematical INTEGER remainder division. Also called Modulo or Modulus, it works as integer remainder division.

Syntax
 remainder = numerator MOD divisor
Parameters
 Returns the integer division remainder as a whole INTEGER, LONG or _INTEGER64 value.
 numerator is the INTEGER value to divide.
 divisor is the INTEGER value to divide by.
Usage:
 Floating decimal point numerator and divisor values are CINT rounded (e.g. 19 MOD 6.7 returns 5 just like 19 MOD 7 would).
 MOD returns 0 if a number is evenly divisible by Integer division ( \ ) or the number divided is 0.
 Divisor (second value) must not be a value of 0 to .5. This will create a "Division by zero" error! due to CINT rounding.
 The result has the same sign as the numerator (e.g. 1 MOD 7 returns 1, not 6).
 Division and multiplication operations are performed before addition and subtraction in Qbasic's order of operations.
Example 1:
I% = 100 \ 9 R% = 100 MOD 9 PRINT "Integer division ="; I%, "Remainder ="; R%
Integer division = 11 Remainder = 1
Explanation: Integer division 100 \ 9 returns 11. 11 * 9 = 99. So the remainder must be 1 as 100  99 = 1. Normal decimal point division would return 11.11111.
Example 2: Comparing normal, integer and remainder division.
tmp1$ = " Normal: ####.# / #### = ##.### " tmp2$ = " Integer: ####.# \ #### = ### " tmp3$ = " Remainder: ####.# MOD #### = #### " FOR i = 1 TO 6 SELECT CASE i CASE 1: numerator = 1: divisor = 5 CASE 2: numerator = 13: divisor = 10 CASE 3: numerator = 990: divisor = 100 CASE 4: numerator = 1100: divisor = 100 CASE 5: numerator = 4501: divisor = 1000 CASE 6: numerator = 50.6: divisor = 10 END SELECT LOCATE 5, 20: PRINT USING tmp1$; numerator; divisor; numerator / divisor LOCATE 7, 20: PRINT USING tmp2$; numerator; divisor; numerator \ divisor LOCATE 9, 20: PRINT USING tmp3$; numerator; divisor; numerator MOD divisor DO: SLEEP: LOOP UNTIL INKEY$ <> "" NEXT
Example 3: Integer division and MOD can be used to convert values to different base numbering systems from base 2 to 36 as strings:
CLS DO INPUT "Enter a base number system 2 to 36: ", b% IF b% < 2 OR b% > 36 THEN EXIT DO PRINT "Enter a positive value to convert: "; num$ = "" DO: K$ = INKEY$ num$ = num$ + K$ LOCATE CSRLIN, POS(0): PRINT K$; LOOP UNTIL K$ = CHR$(13) n& = VAL(num$) IF n& = 0 THEN EXIT DO Bnum$ = BASEN$(n&, b%) PRINT Bnum$ ', VAL("&H" + Bnum$) 'tests hexadecimal base 16 only LOOP END FUNCTION BASEN$ (number&, basenum%) IF basenum% < 2 OR basenum% > 36 OR number& = 0 THEN EXIT FUNCTION num& = number& 'protect value of number! DO remain% = ABS(num&) MOD basenum% ' remainder is used to create actual digit 0 to Z num& = num& \ basenum% ' move up one exponent of base% with integer division IF remain% > 9 THEN b$ = CHR$(65 + (remain%  10)) 'limited to base 36 ELSE: b$ = LTRIM$(STR$(remain%)) ' make remainder a string number END IF BN$ = b$ + BN$ ' add remainder character to base number string LOOP UNTIL num& = 0 BASEN$ = BN$ END FUNCTION
 Note: Base numbering systems over base 10(0  9) use alphabetical letters to represent digits greater than 9 like Hexadecimal(0  F).
See also:
 / (normal division operator)
 \ (integer division operator)
 INT, CINT, FIX, _ROUND
 Mathematical Operations