What is the Test for Divisibility by 2?

S3-SA4-0037

Grade Level:

Class 6

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

Definition

What is it?

The Test for Divisibility by 2 is a quick way to check if a number can be divided by 2 without leaving any remainder. A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8).

Simple Example

Quick Example

Imagine you have 10 cricket balls and you want to divide them equally between two friends. Since 10 ends with a '0' (an even digit), you know immediately that 10 is divisible by 2. Each friend gets 5 balls, with no balls left over.

Worked Example

Step-by-Step

Let's check if the number 734 is divisible by 2.
1. Look at the last digit of the number 734.
2. The last digit is 4.
3. Check if 4 is an even number. Yes, 4 is an even number.
4. Since the last digit (4) is even, the entire number 734 is divisible by 2.
Answer: Yes, 734 is divisible by 2.

Why It Matters

Understanding divisibility rules helps in quickly simplifying calculations, which is crucial in fields like Computer Science for efficient coding and Data Science for processing large datasets. Engineers use these concepts for design calculations, and even in Cryptography, understanding number properties is fundamental for secure communication.

Common Mistakes

MISTAKE: Checking if the first digit is even. For example, thinking 23 is divisible by 2 because 2 is even. | CORRECTION: Always check the LAST digit of the number, not the first or any other digit.

MISTAKE: Confusing odd and even numbers. For example, thinking 5 is an even digit. | CORRECTION: Remember that even numbers are 0, 2, 4, 6, 8. Odd numbers are 1, 3, 5, 7, 9.

MISTAKE: Trying to divide the entire number when the last digit is clearly odd. For example, trying to divide 127 by 2. | CORRECTION: If the last digit is 1, 3, 5, 7, or 9, the number is NOT divisible by 2, so there's no need to perform the full division.

Practice Questions

Try It Yourself

QUESTION: Is the number 456 divisible by 2? | ANSWER: Yes

QUESTION: Which of these numbers is NOT divisible by 2: 102, 345, 678, 900? | ANSWER: 345

QUESTION: A shopkeeper has 59 laddoos. Can he pack them into boxes, with 2 laddoos in each box, without any laddoos left over? | ANSWER: No, because 59 is not divisible by 2 (it ends in 9, an odd digit).

MCQ

Quick Quiz

Which of the following numbers is divisible by 2?

135

247

380

491

The Correct Answer Is:

A number is divisible by 2 if its last digit is even. Only 380 has an even last digit (0). The other numbers end in odd digits (5, 7, 1).

Real World Connection

In the Real World

Imagine you're developing an app like UPI for payments. When splitting a bill equally between two friends, the app needs to quickly check if the total amount is divisible by 2 to ensure no fractions of rupees are left. Or, when managing inventory, a system might check if the number of items can be perfectly divided into pairs for packaging.

Key Vocabulary

Key Terms

DIVISIBLE: Can 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 (0, 2, 4, 6, 8...) | ODD NUMBER: A whole number that is not divisible by 2 (1, 3, 5, 7, 9...)

What's Next

What to Learn Next

Great job learning about divisibility by 2! Now that you understand this basic rule, you're ready to explore 'What is the Test for Divisibility by 3?'. This will help you check numbers even faster and build a strong foundation for more complex math problems.