Checking the divisibility rules

Let us apply the rules to a few concrete numbers.

Example — Checks

• $3471$: sum of the digits $3+4+7+1=15$, divisible by $3$ but not by $9$. So $3471=3\cdot 1157$, with $1157$ still to be factorised.
• $90706$: alternating difference $6-0+7-0+9=22$, divisible by $11$. Check: $90706/11=8246$.
• Is $1932$ divisible by $7$? We compute $193-2\cdot 2=189=27\cdot 7$: yes.

The rules do not give only a “yes/no”: they often provide directly a factor to start from in order to continue the factorisation.

Links

Topics: Numbers and operations
Concepts: Divisibility rules · Divisibility
Skills: Factorise