A factor is a number that divides another number exactly, without leaving any ___.

Remainder

List the factors of 16.

1, 2, 4, 8, and 16

True or False: Every number has at least three factors.

False, every number has at least two factors: 1 and the number itself.

Fill in the blank: The factors of 17 are ___ and ___.

1 and 17

What is the product of 2 and 5, and what are its factors?

The product is 10, and its factors are 1, 2, 5, and 10.

What do you call the numbers obtained by multiplying a given number by integers?

Multiples

Fill in the blank: All the factors of a number are either less than or equal to the ___.

Number

Define a prime number and provide an example.

A prime number is a natural number that has exactly two distinct factors: 1 and itself. An example of a prime number is 13, which can only be factored as 1 × 13.

The number 1 is classified as ___ because it does not meet the criteria for prime or composite numbers.

Neither prime nor composite

Using the Sieve of Eratosthenes, what is the first step in identifying prime numbers?

Write all the numbers from 1 to 100 in a table and cross out 1, as it is not a prime number.

True or False: The number 4 is a prime number.

False. The number 4 is a composite number because it has more than two factors: 1, 2, and 4.

Fill in the blank: A composite number has ___ or more factors.

Two

What distinguishes a composite number from a prime number?

A composite number has more than two distinct factors, while a prime number has exactly two distinct factors: 1 and itself.

What defines twin primes, and provide an example.

Twin primes are pairs of prime numbers that differ by 2. Examples include (3, 5), (5, 7), and (11, 13).

Two natural numbers are said to be co-primes if ___ and provide an example.

They have only '1' as a common factor. Examples include (2, 3), (5, 7), and (3, 4).

True or False: The prime factorization of 20 is 4 x 5.

False. The prime factorization of 20 is 2 x 2 x 5 or 2² x 5.

Fill in the blank: The process of breaking down a composite number into its prime factors is called ___.

Prime factorization.

What is the prime factorization of 120 using the factor tree method?

The prime factorization of 120 is 2 x 2 x 2 x 3 x 5 or 2³ x 3 x 5.

Riddle: I am a number that is only divisible by 1 and myself, but I can pair with another to differ by 2. What am I?

A prime number.

What are the two methods to find the prime factorization of a number?

The two methods are the Factor Tree Method and the Continuous Division Method.