What is the Test for Divisibility by 7?

S3-SA4-0042

Grade Level:

Class 6

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

Definition

What is it?

The Test for Divisibility by 7 is a simple trick or rule that helps us quickly check if a whole number can be divided by 7 without leaving any remainder. If a number is divisible by 7, it means 7 goes into it perfectly, just like 14 is divisible by 7 because 14 / 7 = 2.

Simple Example

Quick Example

Imagine you have 21 laddoos and want to share them equally among 7 friends. Can you do it without any laddoos left over? Yes, because 21 is divisible by 7 (21 / 7 = 3). The divisibility test for 7 helps us find this out quickly for bigger numbers.

Worked Example

Step-by-Step

Let's check if 392 is divisible by 7.
1. Take the last digit of the number. For 392, the last digit is 2.
2. Double the last digit. 2 x 2 = 4.
3. Subtract this doubled number from the remaining part of the original number. The remaining part of 392 is 39. So, 39 - 4 = 35.
4. Now, check if this new number (35) is divisible by 7. We know that 35 / 7 = 5.
5. Since 35 is divisible by 7, the original number 392 is also divisible by 7.
--- So, 392 is divisible by 7.

Why It Matters

Knowing divisibility rules makes calculations faster, which is super useful in competitive exams and everyday problem-solving. In fields like Computer Science and Cryptography, understanding number properties helps in designing efficient algorithms and secure codes. Even in Data Science, quickly filtering data based on divisibility can speed up analysis.

Common Mistakes

MISTAKE: Forgetting to double the last digit before subtracting. | CORRECTION: Always remember to multiply the last digit by 2 before performing the subtraction step.

MISTAKE: Applying the rule only once for large numbers and thinking the result is final. | CORRECTION: If the number after subtraction is still large, you can repeat the divisibility test for 7 on that new number until you get a small, easily recognizable multiple of 7.

MISTAKE: Confusing the divisibility rule for 7 with other numbers like 3 or 9. | CORRECTION: Each number has a unique divisibility rule. The 'double the last digit and subtract' rule is specific to the number 7.

Practice Questions

Try It Yourself

QUESTION: Is 133 divisible by 7? | ANSWER: Yes

QUESTION: Check if 504 is divisible by 7. | ANSWER: Yes, 504 is divisible by 7 (50 - (4x2) = 50 - 8 = 42, and 42 is divisible by 7).

QUESTION: A mobile phone company offers a data pack that renews every 7 days. If you bought it on day 1, on which day will it renew if today is day 287? Is 287 divisible by 7? | ANSWER: Yes, 287 is divisible by 7. (28 - (7x2) = 28 - 14 = 14, and 14 is divisible by 7). It will renew on day 287.

MCQ

Quick Quiz

Which of these numbers is divisible by 7?

121

147

155

163

The Correct Answer Is:

For 147: (14 - (7x2)) = 14 - 14 = 0. Since 0 is divisible by 7, 147 is divisible by 7. The other options do not result in a multiple of 7.

Real World Connection

In the Real World

Imagine you are a programmer working on a train scheduling system for Indian Railways. If a train departs every 7 days, you might use divisibility by 7 to quickly check if a particular date falls on a departure day. This helps in efficient planning and avoiding errors in complex schedules.

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 a division. | MULTIPLE: A number that can be divided by another number a certain number of times without a remainder. | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

What's Next

What to Learn Next

Great job learning about divisibility by 7! Next, you can explore other divisibility rules, like those for 11 or 13. Understanding these rules will make you a pro at number manipulation and mental math, helping you tackle more complex problems with ease.