Strange behavior in ASM (x64 Intel - Linux) with RAX register and DIV instruction

Question

I wrote this code in asm x64 on an Intel processor on Linux and it should counts the number of digits of RDI content and returns the result into RAX. It simply divides RAX by 10 until RAX equals 0 (until quotient equals 0). At each loop, RCX increases :

bits 64
global _start

section .text

_start:
    mov rdi,1234
    
    push rcx
    push rsi
    push rdx

    mov rsi,0xa
    mov rax,rdi
    xor rcx,rcx

func_loop:
    cmp rax,0x0
    jz func_fin
    inc rcx
    div rsi
    jmp func_loop

func_fin:
    mov rax,rcx

    pop rdx
    pop rsi
    pop rcx

    mov rax,0x3c ; sys_exit
    mov rdi,0x0
    syscall

When executed, the program seems to be in an infinite loop... GDB tells me this :

Could you tell me why RAX content is suddenly changing from 123 to 7378697629483820658 ? Did i misunderstand the use of DIV instruction ?

Thank you for all your attention to this.