On this page, you can read information and examples about the divisibility rule of the 9 sign, as well as examples showing how this rule is used. Divisibility by 9 is a short rule that we use to check whether a number is divisible by 9 or not (whether when dividing we get a result that is a whole number or we get a remainder, i.e. a decimal number)!
Divisibility of 9
The rule of divisibility by 9:
A number is divisible by 9 if and only if the sum of its digits is divisible by 9!
The rule clearly shows that to check whether a number is divisible by 9 or not, it is enough to calculate the sum of its digits and check whether that sum is divisible by 9 or not. Moreover, if the number is divisible by 9, we draw the conclusion that the number itself is divisible by 9, while if the sum is not divisible by 9, then the number itself is not divisible by 9.
Solved examples with the rule of divisibility by 9
Check out the solved examples below!
Example 1: Determine (using the rule of divisibility by the number 9) whether the number 972 is divisible by the number 9!
First, we calculate what is the sum of the digits of the number 972!
9 + 7 + 2 = 18
The sum of the digits, the number 18 is divisible by 9, so we deduce that the number 972 must be divisible by 9! If we do an inspection, we get that:
972 : 9 = 108
thus directly confirming that the number 972 is indeed divisible by the number 9!
Example 2: Determine if the number 528 is divisible by the number 9!
First we calculate what is the sum of the digits of the number 528!
5 + 2 + 8 = 15
The sum of the digits, the number 15 is not divisible by 9, so we deduce that the number 528 is not divisible by the number 9! If we do an inspection, we get that:
528 : 9 = 58,(6)
thus directly confirming that the number 528 is indeed not divisible by the number 9!
Video examples
The video below contains more examples with solved problems (examination on specific numbers) using the sign of divisibility by 9!
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Tags: Divisibility, Of 9, Rule
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