# Week 4: Prime Numbers – Day 5

1. The prime decomposition of a number is 2 x 11. What are all possible factors of the number?

2. The prime decomposition of a number is 2 x 3 x 3 x 5. What are all possible factors of the number?

3. The prime decomposition of a number is 2 x 3 x 5 x 7. Is this number divisible by 21?

4. The prime decomposition of a number is 2 x 2 x 5 x 5 x 5. How many zeros are at the right end of the number (in other words, how many multiples of 10 can go into the number)?

5. Sally has opens her book. The product of the two open page numbers is 210. What are the page numbers?

# Week 4: Prime Numbers – Day 4

Prime Decomposition

Positive whole numbers can be written as products of prime numbers, in a unique way from smallest prime factor to largest prime factor.

1. What are the prime factors of 6?

2. What are the prime factors of 42?

3. What are the prime factors of 32?

4. Write the number 45 as a product of primes.

5. Write the number 84 as a product of primes.

# Week 4: Prime Numbers – Day 3

How Many Prime Numbers Are There?

1. How many prime numbers are less than 10?

2. How many prime numbers are between 10 and 20?

3. How many prime numbers are between 20 and 30?

4. How many prime numbers are between 30 and 40?

5. In a group of ten consecutive numbers  > 10, what is the maximum number of primes there could be? (Hint: how many of the ten numbers MUST be even? Knock those out. What other multiples can you eliminate?) It might help to write the numbers down as a list and cross out the possibilities.

# Week 4: Prime Numbers – Day 2

How can you tell if a number is prime?

A prime number has only two factors.

1. Which of the following numbers is divisible by 2 (and definitely not prime)?

17, 26, 101, 924, 1000000, 39

2. Which of the following numbers is divisible by 3 (and definitely not prime)?

16, 51, 39, 243, 117, 2014, 2016

3. Which of the following numbers is divisible by 9 (and definitely not prime)?

16, 51, 39, 72, 243, 117, 2010, 2014, 2016

4. Which of the following numbers is divisible by 7?

18, 28, 43, 45, 49, 52, 63, 72, 87, 91, 98

5. Which of the following numbers is divisible by 15?

16, 51, 39, 72, 243, 117, 2010, 2014, 2016

# Week 4: Prime Numbers – Day 1

A prime number has precisely two distinct (different) factors: itself and 1.

The number 1 is not prime. It has only one factor.

1. How many even prime numbers are there?

2. List all the prime numbers between 10 and 20.

3. What is the name for a whole number > 1 that is not prime?

4. List three consecutive prime numbers.

5. Is it true that the sum of two prime numbers is a prime number?