Unit 1: Number Theory, Day 1
Learning Targets
 I can find all factors of any given
number, less than or equal to 100.
 I can create a list of multiples for any
number less than or equal to 12.
Use all 12 cubes to create as many
different rectangles as you can.
Record your findings by drawing
each rectangle on the grid provided.
What are the dimensions
of each rectangle?
How does the cube activity relate to
finding the factors of a number?
Factor Pair: two numbers that are
multiplied together to produce
another number
Ex 1:
List the factor pairs for 6.
Factor: one of the two numbers being
multiplied together in a factor pair
Ex 2:
List the factors of 6.
Does changing the order of the
numbers in a factor pair change the
product?
**Think about a 3 • 4 and a 4 • 3
rectangle having the same shape..
Commutative Property of
Multiplication:
changing the order of two or more
factors in a multiplication problem
does not change the product
4 • 3 = 12
AND
3 • 4 = 12
How many different rectangles
could you create using 17 cubes?
Prime Number: a number greater
than 1 with exactly two distinct
factors, 1 and the number itself
Factors of 17: 1, 17
Prime numbers have only one
rectangular array.
Composite Number: a number that
has more than two factors
Factors of 12: 1, 2, 3, 4, 6, 12
Composite numbers have two or more
rectangular arrays.
Is the number 1
prime, composite, or neither?
Ex 3:
List the prime numbers from 1-10.
What are the most common prime numbers?
Ex 4:
List the composite numbers from 1-10.
Rainbow Factors
List the factors of the number and connect the factor pairs:
Factors of 24:
Disadvantage:
-With larger numbers, the list could get very long.
Ex 5:
Create rainbow factors for 18.
Prime Factorization: the
expression of a composite number
as a product of prime numbers
2 • 5 • 5 = 50
prime
composite
We can use the factor tree method to find
the prime factorization of a number.
2 • 2 • 3 • 5 = 60
**Always try to start
by factoring out 2,
3, or 5 first
Use a factor tree to write the prime factorization:
Ex 6:
48 -
Ex 7:
81-
We can use the ladder method to find the
prime factorization of a number.
2 36
2 18
3 9
3 3
1
2 • 2 • 3 • 3 = 36
**Always try to start by
dividing first by 2, 3, or 5
Use the ladder method to write the prime
factorization:
Ex 8:
56 -
Ex 9:
72 -
What is a multiple?
Multiple: the product of a given
number and some other number,
except for zero
Ex: Multiples of 10 –
10
20
30
1 • 10
2 • 10
3 • 10
40
50
60
4 • 10
5 • 10
6 • 10
Trick to remember the difference
between factors and multiples:
Factors = Few
Multiples = Many
(multiples DO NOT end)
List the first 10 multiples of:
Ex 10:
2–
Ex 11:
7–