What is the Test for Divisibility by 6?

S3-SA4-0041

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Test for Divisibility by 6 helps us quickly check if a whole number can be divided by 6 without leaving any remainder. A number is divisible by 6 if it is divisible by both 2 and 3.

Simple Example

Quick Example

Imagine you have 48 laddoos and want to pack them into boxes, with 6 laddoos in each box. To know if you can do this perfectly without any laddoos left over, you can use the divisibility test for 6. Since 48 is divisible by 2 (it's an even number) and also by 3 (4+8=12, and 12 is divisible by 3), 48 is divisible by 6. So, you can pack them perfectly!

Worked Example

Step-by-Step

Let's check if the number 138 is divisible by 6.

1. Check for Divisibility by 2: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8. The last digit of 138 is 8, which is an even number.
---2. So, 138 is divisible by 2.
---3. Check for Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 138, the sum of digits is 1 + 3 + 8 = 12.
---4. Since 12 is divisible by 3 (12 / 3 = 4).
---5. So, 138 is divisible by 3.
---6. Conclusion: Since 138 is divisible by both 2 and 3, it is also divisible by 6.

Answer: Yes, 138 is divisible by 6.

Why It Matters

Understanding divisibility rules is super useful in fields like Computer Science for optimizing calculations and in Cryptography for securing data. Engineers use these concepts for design and resource allocation, while data scientists might use them for grouping and categorizing information efficiently.

Common Mistakes

MISTAKE: Only checking if a number is divisible by 2, or only by 3. | CORRECTION: Remember, for a number to be divisible by 6, it MUST be divisible by BOTH 2 and 3.

MISTAKE: Incorrectly adding the digits for the divisibility by 3 test. For example, for 256, saying 2+5+6=14 and then thinking 14 is divisible by 3. | CORRECTION: Always double-check your addition. 14 is not divisible by 3, so 256 is not divisible by 3 (and thus not by 6).

MISTAKE: Thinking that if a number is just an even number, it's divisible by 6. For example, 10 is even, but not divisible by 6. | CORRECTION: Being even only satisfies the 'divisible by 2' part. You still need to check if the sum of its digits is divisible by 3.

Practice Questions

Try It Yourself

QUESTION: Is 72 divisible by 6? | ANSWER: Yes

QUESTION: Which of these numbers is divisible by 6: 104, 216, 305? | ANSWER: 216

QUESTION: A shopkeeper has 150 chocolates. Can he make packs of 6 chocolates each without any left over? Show your working. | ANSWER: Yes. 150 is even (divisible by 2). Sum of digits 1+5+0=6 (divisible by 3). Since it's divisible by both 2 and 3, it's divisible by 6.

MCQ

Quick Quiz

Which of the following numbers is divisible by 6?

124

135

156

170

The Correct Answer Is:

156 is an even number (divisible by 2). The sum of its digits is 1+5+6=12, which is divisible by 3. Since 156 is divisible by both 2 and 3, it is divisible by 6.

Real World Connection

In the Real World

In logistics and supply chain management, like when planning delivery routes for an e-commerce company such as Flipkart or Amazon, understanding divisibility can help in efficiently packing items into standard-sized boxes or vehicles. If a truck can hold items in groups of 6, knowing this rule helps optimize loading without wasted space.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another number without a remainder. | REMAINDER: The amount left over after division. | EVEN NUMBER: A whole number that is divisible by 2. | SUM OF DIGITS: The result of adding all the individual digits of a number together.

What's Next

What to Learn Next

Great job learning about divisibility by 6! Next, you can explore divisibility rules for other numbers like 4, 8, 9, and 11. These rules build on similar logic and will make you even faster at number calculations!