Check if Number is Prime in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Prime Check for 29

What is the output of this TypeScript code that checks if 29 is prime?

DSA Typescript

function isPrime(num: number): boolean {
  if (num <= 1) return false;
  for (let i = 2; i * i <= num; i++) {
    if (num % i === 0) return false;
  }
  return true;
}
console.log(isPrime(29));

A true

B false

C undefined

D SyntaxError

💡 Hint

29 is a prime number because it has no divisors other than 1 and itself.

The function checks divisors up to the square root of 29. Since none divide 29 evenly, it returns true.

❓ Predict Output

intermediate

Output of Prime Check for 1

What is the output of this TypeScript code that checks if 1 is prime?

DSA Typescript

function isPrime(num: number): boolean {
  if (num <= 1) return false;
  for (let i = 2; i * i <= num; i++) {
    if (num % i === 0) return false;
  }
  return true;
}
console.log(isPrime(1));

A true

B false

C TypeError

D 0

💡 Hint

1 is not considered a prime number.

The function returns false immediately for numbers less than or equal to 1.

❓ Predict Output

advanced

Output of Prime Check for 100

What is the output of this TypeScript code that checks if 100 is prime?

DSA Typescript

function isPrime(num: number): boolean {
  if (num <= 1) return false;
  for (let i = 2; i * i <= num; i++) {
    if (num % i === 0) return false;
  }
  return true;
}
console.log(isPrime(100));

A true

B SyntaxError

C false

D undefined

💡 Hint

100 is divisible by 2 and 5.

The function finds that 100 is divisible by 2 and returns false.

❓ Predict Output

advanced

Output of Prime Check for 2

What is the output of this TypeScript code that checks if 2 is prime?

DSA Typescript

function isPrime(num: number): boolean {
  if (num <= 1) return false;
  for (let i = 2; i * i <= num; i++) {
    if (num % i === 0) return false;
  }
  return true;
}
console.log(isPrime(2));

A true

B TypeError

C false

D 0

💡 Hint

2 is the smallest prime number.

The loop condition fails immediately because 2*2 > 2, so the function returns true.

🧠 Conceptual

expert

Why does the prime check loop run only up to the square root?

Why does the prime checking function only test divisors up to the square root of the number?

A Because checking beyond the square root causes runtime errors.

B Because numbers larger than the square root are always prime.

C Because the square root is the largest possible divisor of any number.

D Because any factor larger than the square root would have a matching smaller factor already checked.

💡 Hint

Think about pairs of factors and how they multiply to the number.

If a number has a factor larger than its square root, it must pair with a smaller factor already checked, so checking beyond the square root is unnecessary.

Practice

1. What does it mean for a number to be prime?

easy

A. It is divisible by 2 only.

B. It has more than two divisors.

C. It is an even number greater than 2.

D. It has exactly two distinct positive divisors: 1 and itself.

Solution

1. Step 1: Understand the definition of prime number

   A prime number is a number greater than 1 that has no divisors other than 1 and itself.

2. Step 2: Compare options with the definition

   Only It has exactly two distinct positive divisors: 1 and itself. correctly states this definition.

3. Final Answer:

   It has exactly two distinct positive divisors: 1 and itself. -> Option D

4. Quick Check:

   Prime number = two divisors [OK]

Hint: Prime means only divisible by 1 and itself [OK]

Common Mistakes:

• Thinking even numbers are always prime
• Confusing prime with odd numbers
• Believing prime numbers have multiple divisors

2. Which of the following TypeScript function signatures correctly checks if a number is prime?

easy

A. function isPrime(n: boolean): string

B. function isPrime(n: string): number

C. function isPrime(n: number): boolean

D. function isPrime(): void

Solution

1. Step 1: Identify correct parameter and return types

   The function should take a number and return a boolean indicating prime or not.

2. Step 2: Match options with correct signature

   function isPrime(n: number): boolean matches: input number, output boolean.

3. Final Answer:

   function isPrime(n: number): boolean -> Option C

4. Quick Check:

   Input number, output boolean [OK]

Hint: Input number, output true/false for prime [OK]

Common Mistakes:

• Using wrong input types like string or boolean
• Returning wrong types like number or void
• Missing function parameters

3. What will be the output of the following TypeScript code?

function isPrime(n: number): boolean {
  if (n <= 1) return false;
  for (let i = 2; i <= Math.sqrt(n); i++) {
    if (n % i === 0) return false;
  }
  return true;
}
console.log(isPrime(11));

medium

A. true

B. false

C. undefined

D. SyntaxError

Solution

1. Step 1: Check input and initial condition

   Input is 11, which is greater than 1, so continue checking.

2. Step 2: Loop from 2 to sqrt(11) ≈ 3.3

   Check divisibility by 2 and 3. 11 % 2 != 0 and 11 % 3 != 0, so no divisor found.

3. Final Answer:

   true -> Option A

4. Quick Check:

   11 is prime = true [OK]

Hint: Check divisors up to square root only [OK]

Common Mistakes:

• Checking divisors beyond sqrt(n)
• Returning true too early
• Not handling n <= 1 correctly

4. Identify the error in this TypeScript function to check prime numbers:

function isPrime(n: number): boolean {
  if (n < 2) return false;
  for (let i = 2; i < n / 2; i++) {
    if (n % i === 0) return false;
  }
  return true;
}

medium

A. Loop should run until i <= Math.sqrt(n) for efficiency

B. Return type should be number, not boolean

C. Loop should run until i <= n / 2, not i < n / 2

D. Condition if (n < 2) should be if (n <= 1)

Solution

1. Step 1: Identify the logic error in loop condition

   The loop uses i < n / 2. For n=4, n/2=2, i=2 < 2 false; loop skips check for 2, returns true (but 4 not prime).

2. Step 2: Correct the loop bound

   For efficiency and correctness, the loop should run until i <= Math.sqrt(n) instead of n/2.

3. Final Answer:

   Loop should run until i <= Math.sqrt(n) for efficiency -> Option A

4. Quick Check:

   Loop bound to sqrt(n) is optimal and correct [OK]

Hint: Loop to i <= sqrt(n) for efficient prime check [OK]

Common Mistakes:

• Using i < n/2 instead of i <= n/2 in loop
• Wrong return type
• Incorrect boundary condition for n

5. You want to find all prime numbers between 10 and 20 using this function:

function isPrime(n: number): boolean {
  if (n <= 1) return false;
  for (let i = 2; i <= Math.sqrt(n); i++) {
    if (n % i === 0) return false;
  }
  return true;
}

Which of the following arrays correctly lists these primes?

medium

A. [10, 12, 14, 16, 18, 20]

B. [11, 13, 17, 19]

C. [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]

D. [9, 11, 13, 15, 17, 19]

Solution

1. Step 1: Identify prime numbers between 10 and 20

   Check each number: 11 (prime), 12 (not), 13 (prime), 14 (not), 15 (not), 16 (not), 17 (prime), 18 (not), 19 (prime), 20 (not).

2. Step 2: List only primes in the array

   The primes are 11, 13, 17, and 19.

3. Final Answer:

   [11, 13, 17, 19] -> Option B

4. Quick Check:

   Primes 10-20 = [11,13,17,19] [OK]

Hint: Check each number with isPrime, collect true results [OK]

Common Mistakes:

• Including non-prime even numbers
• Including numbers less than 10 or greater than 20
• Confusing primes with odd numbers