Bell Work: Find the perimeter and area of a rectangle with a length of 12cm and a width of 9cm.

Answer: Perimeter = 42cm Area = 108cm 2

Lesson 9: Prime Numbers

Prime Numbers*: a counting number greater than 1 whose only two factors are the number 1 and itself.

7 is a Prime Number. Its only factors are 1 and is not a Prime Number. Its factors are 1, 2, 5, and 10.

This grid shows 6 x 1. We can also arrange the grid like this. This grid shows 3 x 2. These two rectangles illustrate the two counting number factor pairs of 6.

The grid 7 x 1 however can only form 1 rectangle meaning that it has only 1 factor pair. A prime number can only form a “n x 1” rectangle.

Composite Numbers*: a counting number greater than 1 that can be expressed as a product of prime numbers. Every composite number has 3 or more factors.

9 is divisible by 1, 3 and 9. It is composite. 11 is divisible by 1 and 11. It is not composite.

Prime Factorization*: The expression of a composite number as a product of its prime factors. Prime factorization of 60 is 2 x 2 x 3 x 5

Example: What is the prime factorization of 36 and 45?

Answer: 36 = 2 x 2 x 3 x 3 45 = 3 x 3 x 5

Divisible*: Ability to be divided by a counting number without a remainder.

One way to test if a counting number is prime or composite is to determine if it divisible by a counting number other than 1 and itself.

Divisible Tests ConditionNumber is Divisible by Example using 3420 The number is even (ends in 0, 2, 4, 6, 8)23420 The sum of the digits is divisible by = 9 9 is divisible by 3 The number ends in 0 or

We can combine these tests to build divisibility tests for other numbers. Here are some examples. A number is divisible by 2 and 5 is divisible by 10 (2 x 5). Thus 3420 is divisible of 10. A number is divisible by 2 and 5 is divisible by 10 (2 x 5). Thus 3420 is divisible of 10.

A number divisible by 2 and 3 is divisible by 6 (2 x 3). Thus 3420 is divisible by 6. A number divisible by 2 and 3 is divisible by 6 (2 x 3). Thus 3420 is divisible by 6. A number is divisible by 9 if the sum of its digits is divisible by 9 (3 x 3). Thus 3420 is divisible by 9 because the sum of its digits = 9. A number is divisible by 9 if the sum of its digits is divisible by 9 (3 x 3). Thus 3420 is divisible by 9 because the sum of its digits = 9.

A number is divisible by 4 if its last two digits are divisible by 4. thus 3420 is divisible by 4 since its last two digits (20) are divisible by 4. A number is divisible by 4 if its last two digits are divisible by 4. thus 3420 is divisible by 4 since its last two digits (20) are divisible by 4.

Example: Determine whether the following numbers are prime or composite and state how you know. 1,237,526520,611

Answer: 1,237,526 is composite because because it is even and thus divisible by ,611 is composite because the sum of its digits is divisible by 3. ( = 15) ( = 15)

HW: Lesson 9 #1-30 Due Tomorrow