Number Theory Quiz

Description: This quiz covers various concepts related to number theory, including properties of integers, divisibility, prime numbers, and more. Test your understanding of number theory and its applications.
Number of Questions: 15
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Tags: number theory integers divisibility prime numbers number properties
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Which of the following is a prime number?

  1. 12

  2. 23

  3. 36

  4. 49


Correct Option: B
Explanation:

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Out of the given options, only 23 satisfies this condition.

Find the greatest common divisor (GCD) of 24 and 36.

  1. 6

  2. 8

  3. 12

  4. 18


Correct Option: C
Explanation:

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. For 24 and 36, the GCD is 12.

What is the sum of the first 100 positive integers?

  1. 5050

  2. 5150

  3. 5250

  4. 5350


Correct Option: A
Explanation:

The sum of the first n positive integers is given by the formula n(n+1)/2. For n = 100, the sum is 100(101)/2 = 5050.

Determine if 101 is a prime number.

  1. Yes

  2. No


Correct Option: A
Explanation:

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 101 is only divisible by 1 and 101, making it a prime number.

Which of the following is a factor of 45?

  1. 3

  2. 5

  3. 7

  4. 11


Correct Option: B
Explanation:

A factor of a number is an integer that divides the number without leaving a remainder. 5 is a factor of 45 because 45 ÷ 5 = 9, which is an integer.

Find the least common multiple (LCM) of 12 and 18.

  1. 36

  2. 54

  3. 72

  4. 90


Correct Option: A
Explanation:

The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers. For 12 and 18, the LCM is 36.

What is the value of 2^5?

  1. 16

  2. 32

  3. 64

  4. 128


Correct Option: B
Explanation:

2^5 means 2 raised to the power of 5. This is calculated as 2 × 2 × 2 × 2 × 2, which equals 32.

Determine if 121 is a perfect square.

  1. Yes

  2. No


Correct Option: A
Explanation:

A perfect square is a number that can be expressed as the square of an integer. 121 is a perfect square because it is equal to 11^2.

Find the greatest integer less than 100 that is divisible by both 3 and 5.

  1. 90

  2. 95

  3. 96

  4. 99


Correct Option: A
Explanation:

To find the greatest integer less than 100 that is divisible by both 3 and 5, we can find the least common multiple (LCM) of 3 and 5, which is 15. The greatest integer less than 100 that is divisible by 15 is 90.

Which of the following is a composite number?

  1. 13

  2. 17

  3. 21

  4. 29


Correct Option: C
Explanation:

A composite number is a natural number greater than 1 that has at least one positive divisor other than 1 and itself. 21 is a composite number because it is divisible by 3 and 7.

What is the value of 7! (7 factorial)?

  1. 362880

  2. 5040

  3. 40320

  4. 2520


Correct Option: B
Explanation:

7! (7 factorial) is the product of all positive integers less than or equal to 7. This is calculated as 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals 5040.

Determine if 1001 is a prime number.

  1. Yes

  2. No


Correct Option: B
Explanation:

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 1001 is not a prime number because it is divisible by 7 and 143.

Find the sum of all the factors of 12.

  1. 28

  2. 36

  3. 42

  4. 48


Correct Option: A
Explanation:

The factors of 12 are 1, 2, 3, 4, 6, and 12. The sum of these factors is 1 + 2 + 3 + 4 + 6 + 12 = 28.

Which of the following is a property of prime numbers?

  1. They are divisible by 2.

  2. They have exactly two factors.

  3. They are always odd.

  4. They are always even.


Correct Option: B
Explanation:

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.

What is the value of (-3)^3?

  1. -9

  2. -27

  3. -81

  4. -243


Correct Option: B
Explanation:

(-3)^3 means -3 raised to the power of 3. This is calculated as -3 × -3 × -3, which equals -27.

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