Quick Table of Multiples

[Multiple of 2]
If the last figure of a number is even, then the number is a multiple of 2.

[Multiple of 3]
If the sum of every figure is a multiple of 3, then the number is a multiple of 3.
(Example)
8262; because 8+2+6+2=18 is a multiple of 3, 8362 is a multiple of 3.
(Reason)
8262=8000+200+60+2
=8*(999+1)+2*(99+1)+6*(9+1)+2
=(8*999+2*99+6*9)+(8+2+6+2)
What is firstly parenthesized is a multiple of 3, so you only have to check (8+2+6+2).

[Multiple of 4]
If the last two figures of a number is a multiple of 4, then the number is a multiple of 4.

[Multiple of 5]
If the last figure of a number is 0 or 5, then the number is a multiple of 5.

[Multiple of 9]
If the sum of every figure is a multiple of 9, then the number is a multiple of 9.
(Example)
8262; because 8+2+6+2=18 is a multiple of 9, 8362 is a multiple of 9.
(Reason)
8262=8000+200+60+2
=8*(999+1)+2*(99+1)+6*(9+1)+2
=(8*999+2*99+6*9)+(8+2+6+2)
What is firstly parenthesized is a multiple of 9, so you only have to check (8+2+6+2).

[Postscript]
Aside from the above, there are Quick Tables of Multiples for 7, 11 and 13 which are omitted here due to their poor practicability.

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