5.3: Divisibility Rules

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Amy Lagusker
College of the Canyons

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Divisibility Rules

Table 5.3.1: Divisibility Rules
Divisible by ___?	The Trick!
2	Last digit is even
3	Add up the digits and if the sum is divisible by 3 then so is the original number
4	Divide last 2 digits by 4
5	Ends in 0 or 5
6	Rules for 2 and 3 work
8	Divide last 3 digits by 8
9	Add up the digits and if the sum is divisible by 9 then so is the original number
10	Ends in 0

Example \(\PageIndex{1}\)

What divides evenly into 3495?

Solution

Table 5.3.2
Number	Check it!	Yes or No?
2	Is 3495 even?	no
3	Add the digits: 3 + 4 + 9 + 5 = 21 and 21 divides 3 evenly	yes
4	Can 95 divide 4 evenly?	no
5	Ends in 0 or 5?	yes
6	Divisible by both 2 AND 3?	no
8	Can 495 divide 8 evenly?	no
9	Add the digits: 3 + 4 + 9 + 5 = 21 and 21 does not divide 9 evenly	no
10	Ends in 0?	no

Practice Problems

Test if the numbers in the left column are divisible by the numbers in the top row. Put a “X” in the box where divisibility holds true. Show any work below the table.

Table 5.3.3
	2	3	4	5	6	8	9	10
67820
512
49
3463