(50G) Digits sum (50g)

[Juan14]

The program below finds the sum of the digits of an integer, for example for 236067 the program returns 2+3+6+0+6+7 = 24.

«
0 SWAP
WHILE DUP
REPEAT
10 IDIV2 ROT + SWAP
END DROP
»

If you change the number 10 next the command IDIV2 to 8, you will get the sum of digits of the number in base 8, for example 236067 will return 20 and 236067 in base 8 is 751043, the sum of the digits is 20.

Returning to base 10, you apply the program again and again until you get to single digit number. For example applying successively the program to 7897869769, we get 76, 13 and 4.

I was trying factorials and notice that after 6!, if you reduce to a single digit, this is always 9. I know there are guys out there with better knowledge that can explain this.