Complete the Number: Finding Prime Numbers Ending in 1

Q: Why isn't 51 prime if it ends in 1?

The last digit doesn't determine if a number is prime! 51 = 3 × 17, so it has divisors other than 1 and itself. Always check all possible factors.

Q: What's the difference between prime and composite numbers?

Prime numbers have exactly 2 divisors (1 and themselves). Composite numbers have 3 or more divisors. The number 1 is special - it's neither prime nor composite!

Q: How do I know when to stop checking for factors?

You only need to check divisors up to the square root of your number. For 91, since √91 ≈ 9.5, you only need to test 2, 3, 5, 7, and 9.

Prime Number Identification with Single Digits

Fill in the blank for a prime number:

$\square1$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the blank for a prime number:

$\square1$

Step-by-step solution

To solve the problem, we will follow these steps:

Step 1: List down the potential numbers we can form: 11, 51, 81, and 91.
Step 2: Identify prime numbers by testing divisibility.

Let's analyze each number:

11: The only divisors of 11 are 1 and 11 itself, which makes it a prime number.

51: Check divisibility: 51 is divisible by 3, thus it is not prime because 51 ÷ 3 = 17.

81: Check divisibility: 81 is divisible by 3 (since 8+1=9, which is divisible by 3). So, 81 ÷ 3 = 27, and it is not a prime.

91: Check divisibility further: 91 is divisible by 7 (as 91 ÷ 7 = 13) which makes it not prime.

After examining each option, 11 is the only prime number.

Therefore, the solution to the problem is $11$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Prime Definition: A number with exactly two divisors: 1 and itself
Technique: Test divisibility: $51 ÷ 3 = 17$ shows 51 is not prime
Check: Verify 11 has only divisors 1 and 11 itself ✓

Common Mistakes

Avoid these frequent errors

Assuming larger numbers are always prime
Don't think 91 must be prime just because it's bigger = wrong answer! Large numbers often have hidden factors like 91 = 7 × 13. Always test divisibility systematically by checking small prime factors first.

Practice Quiz

Test your knowledge with interactive questions

Is the number equal to $$ n $$ prime or composite?

$$ n=10 $$

FAQ

Everything you need to know about this question

How do I quickly check if a two-digit number is prime?

Test divisibility by small primes: 2, 3, 5, 7, 11. If the number isn't divisible by any of these (up to its square root), it's prime!

Why isn't 51 prime if it ends in 1?

The last digit doesn't determine if a number is prime! 51 = 3 × 17, so it has divisors other than 1 and itself. Always check all possible factors.

Is there a trick for checking divisibility by 3?

Yes! Add up all the digits. If that sum is divisible by 3, then the original number is too. For 81: 8 + 1 = 9, and 9 ÷ 3 = 3, so 81 is divisible by 3.

What's the difference between prime and composite numbers?

Prime numbers have exactly 2 divisors (1 and themselves). Composite numbers have 3 or more divisors. The number 1 is special - it's neither prime nor composite!

How do I know when to stop checking for factors?

You only need to check divisors up to the square root of your number. For 91, since √91 ≈ 9.5, you only need to test 2, 3, 5, 7, and 9.

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