What is the Test for Divisibility by 4?

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Grade Level:

Class 6

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

Definition

What is it?

The Test for Divisibility by 4 is a quick trick to check if a whole number can be divided by 4 evenly, without leaving any remainder. You only need to look at the last two digits of the number to decide.

Simple Example

Quick Example

Imagine you have 124 cricket balls and want to divide them equally among 4 teams. Instead of actually dividing, you can just look at the last two digits of 124, which are '24'. Since 24 can be divided by 4 (24 / 4 = 6), then 124 is also divisible by 4. So, yes, you can divide the balls equally!

Worked Example

Step-by-Step

Let's check if the number 7,356 is divisible by 4.
---Step 1: Identify the last two digits of the number. For 7,356, the last two digits are 56.
---Step 2: Check if the number formed by these last two digits is divisible by 4. Is 56 divisible by 4?
---Step 3: Perform the division: 56 ÷ 4.
---Step 4: 56 ÷ 4 = 14. Since 14 is a whole number and there is no remainder, 56 is divisible by 4.
---Step 5: Because the number formed by the last two digits (56) is divisible by 4, the original number (7,356) is also divisible by 4.
Answer: Yes, 7,356 is divisible by 4.

Why It Matters

Understanding divisibility rules helps computer scientists write efficient code for calculations and is crucial in cryptography for secure data. Engineers use these rules when designing systems that need to distribute resources evenly. It's a fundamental skill for anyone working with numbers, from data analysis to financial planning.

Common Mistakes

MISTAKE: Checking only the last digit to see if it's even. | CORRECTION: The divisibility rule for 4 requires you to look at the *last two digits*, not just the last one. A number ending in 2 (like 122) is even, but not divisible by 4.

MISTAKE: Trying to divide the entire large number by 4 manually. | CORRECTION: The whole point of the rule is to save time! Just focus on the number formed by the last two digits. If that smaller number is divisible by 4, the big number is too.

MISTAKE: Getting confused when the last two digits are '00' (e.g., 500). | CORRECTION: If the last two digits are '00', the number is always divisible by 4. Think of it as 00 being divisible by 4 (0 / 4 = 0).

Practice Questions

Try It Yourself

QUESTION: Is 872 divisible by 4? | ANSWER: Yes

QUESTION: A mobile data pack gives you 1500 MB. Can this be perfectly divided into 4 equal parts for different apps? | ANSWER: No (1500 ends in 00, which is divisible by 4, so yes, it can be divided. My mistake in the answer generation. The correct answer should be Yes. Let's correct this.) | Corrected Answer: Yes

QUESTION: Which of these numbers is NOT divisible by 4: 204, 518, 936, 1200? | ANSWER: 518

MCQ

Quick Quiz

Which of the following numbers is divisible by 4?

342

750

1064

2130

The Correct Answer Is:

For 1064, the last two digits are 64. Since 64 ÷ 4 = 16, 1064 is divisible by 4. For the other options, 42, 50, and 30 are not divisible by 4.

Real World Connection

In the Real World

When a company like ISRO plans to launch satellites, they often need to allocate resources like fuel or time in precise, divisible chunks. Or imagine a payment system like UPI processing millions of transactions: quickly checking divisibility helps in grouping transactions efficiently for processing, ensuring smooth operation and avoiding errors.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another number without leaving a remainder. | REMAINDER: The amount left over after a division when one number cannot be divided exactly by another. | WHOLE NUMBER: A number without fractions or decimals, including zero and positive integers. | LAST TWO DIGITS: The tens and units digits of a number.

What's Next

What to Learn Next

Great job understanding divisibility by 4! Next, you can explore the 'Test for Divisibility by 8'. It's similar but looks at more digits, building directly on what you've learned here and helping you handle even larger numbers with ease.