Divisibility Rule of 162
2026-02-28 08:58 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine whether a number is divisible by another number without performing division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 162.

What is the Divisibility Rule of 162?

The divisibility rule for 162 is a method by which we can find out if a number is divisible by 162 without using the division method. Let's check whether 2916 is divisible by 162 using the divisibility rule.
 

Step 1: Check if the number is divisible by 2, 3, and 9. A number is divisible by 162 if it is divisible by 2, 3, and 9.

For divisibility by 2, the last digit of the number should be even. Here, 6 is even.

For divisibility by 3, the sum of the digits should be a multiple of 3. Here, 2 + 9 + 1 + 6 = 18, and 18 is a multiple of 3.

For divisibility by 9, the sum of the digits should be a multiple of 9. Here, 18 is a multiple of 9.

Step 2: Since 2916 satisfies all three conditions, it is divisible by 162.
 

Tips and Tricks for Divisibility Rule of 162

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 162.
 

  • Know the multiples of 162: Memorize the multiples of 162 (162, 324, 486, 648, etc.) to quickly check divisibility. If the result from the checks is a multiple of 162, then the number is divisible by 162.
     
  • Check divisibility by 2, 3, and 9: Ensure the number meets all three conditions for divisibility by 2, 3, and 9 to confirm divisibility by 162.
     
  • Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them verify their work and also learn.
     

Common Mistakes and How to Avoid Them in Divisibility Rule of 162

The divisibility rule of 162 helps us quickly check if a given number is divisible by 162, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.

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Problem 1

Is the number of seats in a theater, 648, divisible by 162?

Okay, lets begin

Yes, 648 is divisible by 162.

Explanation

To determine if 648 is divisible by 162, we can apply the divisibility rule:

1) Break down the number into parts that can easily be divided by 162, such as 162 × 4 = 648.

2) Since 648 is the product of 162 and an integer, 4, it is divisible by 162.

Well explained 👍

Problem 2

A factory produces 1,458 widgets in a day. Can these widgets be packed equally into boxes of 162 each?

Okay, lets begin

Yes, 1,458 is divisible by 162.

Explanation

To check if 1,458 can be divided equally into boxes of 162:

1) Divide 1,458 by 162, which gives 9.

2) Since 1,458 divided by 162 results in a whole number, 9, the widgets can be packed equally.

Well explained 👍

Problem 3

Is a library's collection of 324 books divisible by 162?

Okay, lets begin

Yes, 324 is divisible by 162.
 

Explanation

To determine divisibility:

1) Divide 324 by 162, which gives 2.

2) Since the division results in a whole number, 2, 324 is divisible by 162.

Well explained 👍

Problem 4

A school event has 972 participants. Can they be grouped into teams of 162?

Okay, lets begin

Yes, 972 is divisible by 162.

Explanation

To verify:

1) Divide 972 by 162, which gives 6.

2) The result is a whole number, hence 972 can be divided equally into groups of 162.

Well explained 👍

Problem 5

A shipment contains 486 items. Can these items be organized into stacks of 162?

Okay, lets begin

No, 486 is not divisible by 162.

Explanation

To check:

1) Divide 486 by 162, which gives approximately 3. 

2) Since the result is not a whole number, 486 cannot be divided equally into stacks of 162.

Well explained 👍

FAQs on Divisibility Rule of 162

1.What is the divisibility rule for 162?

The divisibility rule for 162 is that a number must be divisible by 2, 3, and 9 to be divisible by 162.

2.How many numbers between 1 and 1000 are divisible by 162?

There are 6 numbers between 1 and 1000 that are divisible by 162. They are 162, 324, 486, 648, 810, and 972.
 

3.Is 324 divisible by 162?

Yes, because 324 is a multiple of 162 (162 × 2 = 324).

4.What if I find a number not divisible by 2, 3, or 9?

If a number is not divisible by 2, 3, or 9, it is not divisible by 162.
 

5.Does the divisibility rule of 162 apply to all integers?

Yes, the divisibility rule of 162 applies to all integers.

Important Glossaries for Divisibility Rule of 162

  • Divisibility Rule: The set of rules used to determine whether a number is divisible by another number without performing division.
     
  • Multiple: A multiple is the result of multiplying a number by an integer. For example, multiples of 162 are 162, 324, 486, etc.
     
  • Even Number: A number divisible by 2. For example, 4, 6, and 8 are even numbers.
     
  • Sum of Digits: The total obtained by adding all the digits of a number. For example, the sum of the digits of 2916 is 2 + 9 + 1 + 6 = 18.
     
  • Integer: Whole numbers including positive, negative numbers, and zero.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.