Divisibility Rule By 9 Tested with examples

There is a new divisibility rule by 9 that I just derived which I like to share in this post. The new rule is tested with numbers that are multiples of 9 to show that it works for all numbers that are divisible by 9.

The New Rule:

A number is divisible by 9 if the SUM of the unit digit and the number formed by the rest digits is a multiple of 9

This is what it means: if you have 162, the unit digit is 2 and the number formed by the rest digit is 16.

Below are three examples to test this rule

Example 1: Test 153 for divisibility by 9
To use the rule, split the 153 into 15 and 3
Adding the numbers: 15 + 3
Result: 18 which is 9 x 2
Since 18 is divisible by 9, therefore, 153 is divisible by 9

Example 2: Test 414
Split 414 into 41 and 4
Adding: 41 + 4 = 45
45 = 9 x 5
Since 45 is divisible by 9, therefore, 414 is divisible by 9

Example 3: Test 7101
Split 7101 into 710 and 1
Adding: 710 + 1 = 711
If the sum is too high to determine if it’s a multiple of 9, like 711 above, repeat the steps for the rule on this new number –
Split 711 into 71 and 1
Adding: 71 + 1= 72
72 = 9 x 8 which is a multiple of 9
Since 72 is divisible by 9, therefore, 7101 is divisible by 9

Have fun with this new rule as you test for multiples of 9

Contact me if you have any question

Divisibility Rules for numbers 2 to 10

Introduction

Divisibility rules involve finding out without actually dividing whether a given whole number is a factor of another whole number.

Many textbooks that have this topics states the following rules:

Any whole number is exactly divisible by:

   – 2 if its last digit is even
   – 3 if the sum if its digits form a number divisible by 3
   – 4 if the last two digits form a number divisible by 4
   – 5 if the last digit is 5 or 0
   – 6 If its last digit is even and the sum of its digits form a number divisible by 3
   – 8 if the last three digits form a number divisible by 8
   – 9 if the sum of the digits is divisible by 9
   – 10 if the last digit is 0