Number Theory Quiz

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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