Test: Prime Time - 2 - Class 6 MCQ

Factors of 24:

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Now let's check each option:

• A: 3 is a factor of 24 because 24 ÷ 3 = 8 (no remainder).
• B: 5 is not a factor of 24 because 24 ÷ 5 = 4.8 (remainder).
• C: 7 is not a factor of 24 because 24 ÷ 7 ≈ 3.43 (remainder).
• D: 9 is not a factor of 24 because 24 ÷ 9 ≈ 2.67 (remainder).

The correct answer is: A: 3

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

Let's check each option:

• A: 8 is not a prime number because it can be divided by 1, 2, 4, and 8.
• B: 9 is not a prime number because it can be divided by 1, 3, and 9.
• C: 11 is a prime number because it can only be divided by 1 and 11.
• D: 12 is not a prime number because it can be divided by 1, 2, 3, 4, 6, and 12.

The correct answer is: C: 11.

The common factors of two numbers are the numbers that divide both of them evenly.

Let's find the factors of each number:

• Factors of 7: 1, 7
• Factors of 9: 1, 3, 9

The only common factor between 7 and 9 is 1.

The correct answer is: C: 1.

A composite number is a number that has more than two factors, meaning it is divisible by numbers other than 1 and itself.

Let's check each option:

• A: 5 is a prime number, not composite, because it only has two factors: 1 and 5.
• B: 7 is a prime number, not composite, because it only has two factors: 1 and 7.
• C: 11 is a prime number, not composite, because it only has two factors: 1 and 11.
• D: 12 is a composite number because it has more than two factors: 1, 2, 3, 4, 6, and 12.

The correct answer is: D: 12.

Two numbers are co-prime (also known as relatively prime) if their greatest common divisor (GCD) is 1, meaning they have no common factors other than 1.

Let's check each pair:

• A: 8 and 12:

  • Factors of 8: 1, 2, 4, 8
  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Common factors: 1, 2, 4
  • GCD is 4, so they are not co-prime.

• B: 14 and 21:

  • Factors of 14: 1, 2, 7, 14
  • Factors of 21: 1, 3, 7, 21
  • Common factors: 1, 7
  • GCD is 7, so they are not co-prime.

• C: 9 and 28:

  • Factors of 9: 1, 3, 9
  • Factors of 28: 1, 2, 4, 7, 14, 28
  • Common factor: 1
  • GCD is 1, so they are co-prime.

• D: 15 and 20:

  • Factors of 15: 1, 3, 5, 15
  • Factors of 20: 1, 2, 4, 5, 10, 20
  • Common factors: 1, 5
  • GCD is 5, so they are not co-prime.

The pair that is co-prime is: C: 9 and 28.

To find the prime factorization of 12, we break it down into prime numbers:

1. Start by dividing 12 by the smallest prime number, which is 2:
   12 ÷ 2 = 6
2. Now divide 6 by 2:
   6 ÷ 2 = 3
3. Finally, 3 is a prime number.

The prime factorization of 12 is: 2 × 2 × 3

The correct answer is: A: 2 × 2 × 3

To determine which of these numbers is divisible by both 2 and 3, we need to check the divisibility rules for 2 and 3:

• A number is divisible by 2 if it is even.
• A number is divisible by 3 if the sum of its digits is divisible by 3.

Checking each option:

• A: 4: 4 is even, so divisible by 2.
  The sum of the digits of 4 is 4, which is not divisible by 3.
  So, not divisible by both 2 and 3.
• B: 9: 9 is not even, so not divisible by 2.
  The sum of the digits of 9 is 9, which is divisible by 3, but not divisible by 2.
  So, not divisible by both 2 and 3.
• C: 12: 12 is even, so divisible by 2.
  The sum of the digits of 12 is 3, which is divisible by 3.
  So, divisible by both 2 and 3.
• D: 15: 15 is not even, so not divisible by 2.
  The sum of the digits of 15 is 6, which is divisible by 3, but not divisible by 2.
  So, not divisible by both 2 and 3.

The number that is divisible by both 2 and 3 is: C: 12

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

• A: 1 is not a prime number because it only has one divisor (itself).
• B: 2 is the smallest prime number because its only divisors are 1 and 2.
• C: 3 is a prime number, but it is greater than 2.
• D: 5 is a prime number, but it is greater than 2.

The smallest prime number is: B: 2.

A number is a multiple of 5 if it ends in either 0 or 5.

Let's check each option:

• A: 10 ends in 0, so it is a multiple of 5.
• B: 20 ends in 0, so it is a multiple of 5.
• C: 30 ends in 0, so it is a multiple of 5.
• D: 32 ends in 2, so it is not a multiple of 5.

The number that is not a multiple of 5 is: D: 32.

To find the Least Common Multiple (LCM) of 3 and 5, we look for the smallest number that both 3 and 5 divide into evenly.

Steps:

1. The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
2. The multiples of 5 are: 5, 10, 15, 20, 25, 30, ...

The smallest multiple that appears in both lists is 15.

The LCM of 3 and 5 is: C: 15.