Divisibility, Prime Numbers, and Prime Factorization

The video tutorial introduces the concept of divisibility, explaining how numbers can be divided evenly by certain other numbers. It then defines prime numbers as those with no factors other than 1 and themselves, providing examples and explaining why only odd numbers, except for 2, can be prime. The tutorial also covers prime factorization, demonstrating how to break down numbers into their prime components and explaining the fundamental theorem of arithmetic, which states that each number has a unique set of prime factors.

Which of the following numbers is NOT a factor of 10?

• 1

• 2

• 3

• 5

What is the smallest prime number?

• 3

• 2

• 4

• 1

Why can't even numbers, except for 2, be prime?

• They are all odd numbers

• They have more than two factors

• They are all greater than 10

• They are all divisible by 2

What is a characteristic of prime numbers?

• They are always odd

• They are greater than 10

• They have exactly two distinct positive divisors

• They are always even

What is the significance of the largest prime number discovered?

• It is divisible by 10

• It has millions of digits

• It is the only prime number

• It is the smallest prime number

What is the prime factorization of 36?

• 2 x 3 x 6

• 2 x 2 x 3 x 3

• 2 x 2 x 2 x 3

• 3 x 3 x 4

What does the fundamental theorem of arithmetic state?

• Every number has a unique set of prime factors

• Every number is a prime number

• Every number is even

• Every number is divisible by 1