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Divisibility Rule of 9

A number is said to be divisible by another number if the remainder of the number is a zero(0). Divisibility rules are often used to determine, if a number is evenly divisible by another number or not very easily without doing the actual division. In this article, we are going to discuss the divisibility rule of 9.

Divisibility Rules

Divisibility rules are a set of general rules, often used to determine whether a number is evenly divisible by another number or not.

Although there are divisibility tests for numbers in any base, they are all different.

Here, presents rules and examples only for a decimal or base 10 numbers. 

Martin Gardner explained and popularized rules in his “Mathematical Games, September 1962” column of Scientific American.

Martin Gardner - Explained Divisibility Rule
Martin Gardner (Source)

He was best known for creating sustaining interest in recreational mathematics principally through his “Mathematical Games” columns, throughout the latter half of the 20th century.

This column lasted for 25 years and was avidly read by the generation who grew up in the years 1956 to 1981.

Divisibility Rule of 9 With Examples

The divisibility rule of 9 is the same as for the 3, i.e.

If the sum of the digits is divisible by nine, then the number will be divisible by 9.

Examples:

  1. \(\bf{1827 \div 9}\)
    If we add 1 + 8 + 2 + 7 = 18 which is divisible by 9
    Therefore, the no. 1827 will be divisible by 9
    \(1827 \div 9 = 203\)
  2. \(\bf{91 \div 9}\)
    If we add the no. we get
    9 + 1 = 10 which is not divisible by 9 
    Therefore, 9 is not perfectly divisible by 9
    \(91 \div 9 = 10.11\)

FAQs

What is the divisibility rule of 9?

If the sum of the digits is divisible by nine, then the number will be divisible by 9.

What is the divisibility rule of 3?

If the sum of all of the digits is divisible by three, the number is divisible by 3.

Who was Martin Gardner?

Martin Gardner was best known for creating sustaining interest in recreational mathematics principally through his “Mathematical Games” columns.

Are numbers divisible by 9 divisible by 3?

Since 9 is divisible by 3. The number divisible by 9 is also divisible by 3.

Know More Divisibility Rules:

Divisibility Rule of 7Divisibility Rule of 5
Divisibility Rule of 6

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