Download Notes 1.5 – Factors and Divisibility Patterns

Notes 1.5 – Factors and
Divisibility Patterns
I. Review
Natural Numbers: 1, 2,3, 4,...
Whole Numbers: 0,1, 2,3, 4,...
Integers: ..., 2, 1, 0,1, 2,...
1
Divisible

What does it mean for one number to divide
evenly into another?


What is the remainder when 8 is divided by 3?


When you divide the numbers the remainder is 0.
2
What does the remainder have to do with
divisibility?

If the remainder is zero then the number is divisible
by the divisor.
Modeling Divisibility:
Arrange 6 tokens in a rectangle with 2 rows to
show that 6 is divisible by two.
2
More Modeling

Use tokens to show 7 divided by 2.
Factors
A number is a _______
factor of a given number if it
________
divides into the second number ________.
evenly
Example:
1) Which of the following numbers are factors of
12?
a) 24
b) 3
c) 12
d) 4
e) 5
3
2) Name the other factors of 12:
1,2, and 6
3) What are the factors of 48?
1,2,3,4,6,8,12,16,24,48
______
and the ___________
NUMBER itself are factors of
1
any given number.
Eric rents a booth at a crafts fair. He is allowed to set up 36
square feet in any way that he wants. Eric decides to make
his booth 9 feet long and 4 feet wide.
1) What is the total area of Eric’s booth?
A  4 9  36
a) A = lw
b) Using only natural numbers what are all the
possible side that Eric’s booth could have?
w
l
A
1
36
36
2
3
18
36
12
36
4
6
9
6
36
36
4
Primes, Composites, and Squares
A _________
PRIME number is a natural number with
exactly two factors, itself and one.
A ____________number
is a natural number that is
COMPOSITE
greater than 2 and is not prime.
A composite number has more than ____
2 factors.
Examples
1) Circle the following numbers that are prime:
a) 51
b) 37
c) 2
d) 1
e) 17
2) Circle the composite numbers:
a.) 21
b) 17
c) 50
d) 39
e) 1
(_____
is the only number that is neither prime nor
1
composite.)
5
3) What are the factors of 19? Is it prime or
composite?
1,19
PRIME
4) What are the first ten prime numbers?
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29
What are the factors of 4?
How many factors does it have?
1,2,4
3
1,5,25
What are the factors of 25?
How many factors does it have?
3
What are the factors of 36? 1,2,3,4,6,9,12,18,36
9
How many factors does it have?
A _________
SQUARE number has an odd number of factors and
can be represented as a square with an area equal to
the square number.
6
Divisibility Patterns
Pattern
Examples
Div. by 2
Last digit is even
Div. by 10
Last digit is 0
10, 140, 900
Div. by 5
Last digit is 0 or 5
10, 145, 980
Div. by 3
Sum of digits is  by 3
27, 96, 144
Div. by 6
 by 2 and 3
42, 132, 960
Div. by 9
Sum of digits is  by 9
4, 38, 490
72, 144, 945
Homework:
pages 41-42#’s 1, 2, 4, 6-8, 10-42 even.
7