What is the Divisibility Rule for 17?

S3-SA4-0333

Grade Level:

Class 6

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

Definition

What is it?

The Divisibility Rule for 17 helps us check if a number can be divided by 17 completely, without leaving any remainder. It's a quick trick to avoid long division and see if 17 is a factor of that number.

Simple Example

Quick Example

Imagine your cricket team scored 170 runs. Is 170 divisible by 17? Yes, because 17 x 10 = 170. But what about 173 runs? The divisibility rule helps us figure this out quickly without doing a full division sum.

Worked Example

Step-by-Step

Let's check if 391 is divisible by 17.
1. Take the last digit of the number: It's 1.
---2. Multiply this last digit by 5: 1 x 5 = 5.
---3. Subtract this result from the remaining part of the number (the number without its last digit): The remaining part is 39. So, 39 - 5 = 34.
---4. Now, check if this new number (34) is divisible by 17: Yes, 34 is divisible by 17 (17 x 2 = 34).
---5. Since 34 is divisible by 17, the original number, 391, is also divisible by 17.
ANSWER: Yes, 391 is divisible by 17.

Why It Matters

Understanding divisibility rules is super useful in fields like Computer Science for writing efficient code, or in Cryptography for securing online data. Engineers use these concepts for calculations, and even Data Scientists apply similar logic to sort and analyze large datasets. It's a foundational skill for many future careers!

Common Mistakes

MISTAKE: Multiplying the last digit by a wrong number, like 2 or 3, instead of 5. | CORRECTION: Always remember to multiply the last digit by 5 for the Divisibility Rule of 17.

MISTAKE: Adding the result instead of subtracting it from the remaining number. | CORRECTION: The rule specifically requires you to subtract the multiplied last digit from the rest of the number.

MISTAKE: Not repeating the process if the resulting number is still large. | CORRECTION: If after the first step, the new number is still big, you can repeat the same 'multiply by 5 and subtract' process until you get a number small enough to easily check for divisibility by 17.

Practice Questions

Try It Yourself

QUESTION: Is 204 divisible by 17? | ANSWER: Yes (20 - (4 x 5) = 20 - 20 = 0. 0 is divisible by 17.)

QUESTION: Check if 578 is divisible by 17. | ANSWER: Yes (57 - (8 x 5) = 57 - 40 = 17. 17 is divisible by 17.)

QUESTION: Using the rule, determine if 1071 is divisible by 17. | ANSWER: Yes (107 - (1 x 5) = 102. Then, 10 - (2 x 5) = 10 - 10 = 0. 0 is divisible by 17.)

MCQ

Quick Quiz

Which of the following numbers is divisible by 17?

153

162

171

180

The Correct Answer Is:

For 153: 15 - (3 x 5) = 15 - 15 = 0. Since 0 is divisible by 17, 153 is divisible by 17. Other options do not result in a number divisible by 17.

Real World Connection

In the Real World

Divisibility rules are like shortcuts that computers use for quick checks! For instance, when you see your mobile data usage, apps often need to perform quick calculations to see if a certain amount of data (say, 17GB) fits evenly into a larger plan. In banking, large transaction IDs might be checked for divisibility by certain numbers to ensure data integrity, similar to how UPI transactions are processed quickly and securely.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another without a remainder. | REMAINDER: The amount left over after a division when the divisor does not divide the dividend exactly. | FACTOR: A number that divides another number completely, leaving no remainder. | RULE: A method or trick to quickly check a mathematical property.

What's Next

What to Learn Next

Great job learning the Divisibility Rule for 17! Next, you can explore other divisibility rules, like for 19 or 23. Understanding these will make you even faster at number crunching and build a strong foundation for more advanced math concepts like prime factorization!