Find the Missing Digit: Complete _2 to Make a Prime Number

Q: Why is 2 considered prime when it's even?

2 is the only even prime number! It only has two divisors: 1 and 2. All other even numbers have at least three divisors (1, 2, and themselves), so they're composite.

Q: What does 02 mean as a number?

The number 02 is exactly the same as 2. Leading zeros don't change a number's value - they're just placeholders. So □2 with 0 gives us the prime number 2.

Q: Do I need to check all digits 0 through 9?

In problems like this, yes! Check each digit systematically. For □2, you'd test: 12, 22, 32, 42, 52, 62, 72, 82, 92, and 02 (which is 2).

Q: How do I quickly tell if a two-digit number ending in 2 is prime?

Numbers ending in 2 are usually not prime because they're divisible by 2. The only exception is 2 itself! So for □2, only when □ = 0 do we get a prime.

Q: What if multiple digits work?

Great thinking! Always check all possibilities first. In this case, only 0 works because 2 is the only prime number ending in 2. Other digits give composite numbers like 12, 22, 32, etc.

Prime Number Recognition with Missing Digits

Fill in the blank for a prime number:

$\square2$

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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:

$\square2$

Step-by-step solution

To solve the problem of finding the missing digit in $\square2$ that results in a prime number, we need to check each possible digit from $0$ to $9$ and see which of them make $\square2$ a prime number.

Let's perform this step-by-step analysis:

Step 1: Substitute $0$ in place of $\square$ , resulting in the number $02$ which should be considered as $2$ .
Step 2: Check if the number $2$ is a prime number. A prime number is one that has no divisors other than $1$ and itself.
Step 3: Determine if $2$ is prime. Since $2$ is divisible by only $1$ and $2$ , it is a prime number.

Upon examining the possibilities, the use of $0$ in $\square$ results in $02$ , which is equal to $2$ , a prime number. Therefore, the missing digit that makes $\square2$ a prime number is $0$ .

Thus, the correct number is $02$ or $2$ , and therefore the correct choice from the given options is $0$ .

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Prime Definition: Numbers divisible only by 1 and themselves
Technique: Test each digit 0-9 in □2 systematically
Check: Verify 2 has exactly two divisors: 1 and 2 ✓

Common Mistakes

Avoid these frequent errors

Forgetting that 02 equals 2
Don't ignore leading zeros when evaluating numbers = missing the correct answer! Leading zeros don't change a number's value, so 02 is just 2. Always simplify numbers by removing leading zeros before checking if they're prime.

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

Why is 2 considered prime when it's even?

2 is the only even prime number! It only has two divisors: 1 and 2. All other even numbers have at least three divisors (1, 2, and themselves), so they're composite.

What does 02 mean as a number?

The number 02 is exactly the same as 2. Leading zeros don't change a number's value - they're just placeholders. So □2 with 0 gives us the prime number 2.

Do I need to check all digits 0 through 9?

In problems like this, yes! Check each digit systematically. For □2, you'd test: 12, 22, 32, 42, 52, 62, 72, 82, 92, and 02 (which is 2).

How do I quickly tell if a two-digit number ending in 2 is prime?

Numbers ending in 2 are usually not prime because they're divisible by 2. The only exception is 2 itself! So for □2, only when □ = 0 do we get a prime.

What if multiple digits work?

Great thinking! Always check all possibilities first. In this case, only 0 works because 2 is the only prime number ending in 2. Other digits give composite numbers like 12, 22, 32, etc.

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