Download Estimating With Whole Numbers

Divisibility
Factors and Primes
Unit 4.1 and 4.2
Pages 156-163
Warm Up
Problems
Find how many digits you can multiply
together to create this number.
1. 48 = 1 x 20, 2 x 24, 4 x 5
2. 16 = 1 x 16, 2 x 8, 4 x 4
3. 19 = 1 x 19
4. 85 = 1 x 18, 5 x 17
Divisibility, Prime Factorization.
Objective:
Students will use divisibility rules
to determine if the number is prime or
composite. They will then be able to break it
into factors of prime numbers.
Definitions:
DIVISIBLE: a number is divisible when it has
no remainder left.
42 girls have signed up to play soccer this year. They only
have 6 teams. Is it possible to have an equal amount of
girls on each team?
We need to split all the girls evenly into six groups.
We will use Division to tell if this is possible.
7
6 42
-42
When there is no remainder we are able to say 42
is divisible by 6.
There are tricks to help up decide if a number is
divisible by the numbers: 2, 3, 4, 5, 6, 7, 9. 10.
We only use digital sum for 3’s and 9’s… not for twos and not for 5’s , not for 4’s and 7’s prime and that’s how I know divisibility rules. (sung to the ants go marching)
2 3,9 4 5 6 7
Ends in
2, 4,
6, 8,
0
Add up the
ends in Divisible
Divisible
digits.
by
Divisible by
3 or 9
by
4
5, 0 2, 3
Prime
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
What numbers are
610
divisible by?
2
5
0
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
What numbers are
387
divisible by?
3
9
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
#1) What numbers are
508
divisible by?
2
4
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
#2) What numbers are
432
2
divisible by?
3
4
6
9
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
#4) What numbers are
189
divisible by?
3
9
2
Ends in an even
number.
3,9
Digits add up to be
divisible by 3 or 9.
Divisible by
The number 4.
Ends in a number
5 or 0.
Divisible by the
Number 6.
4
5
6
7 Prime
0 Ends in a zero.
#3) What numbers are
247
divisible by?
none
List all the factors of
18 =
1, 2, 3, 6, 9, 18
First we list all the factors in pairs.
18
1
18
9
2
3
6
4
5
List all the factors of
13 =
1, 13
First we list all the factors in pairs.
13
1
2
3
4
5
6
7
8
13
9
10
11
12
#1) List all the factors of
12 = 1, 2, 3, 4, 6, 12
First we list all the factors in pairs.
12
1
2
3
4
5
6
7
8
9
10
11
12
#2) List all the factors of
21 = 1, 3, 7, 21
First we list all the factors in pairs.
1
2
3
4
5
21
6
7
8
9
10
11
12
#3) List all the factors of
=
First we list all the factors in pairs.
1
2
3
4
5
1, 2, 4, 13, 26, 52
52
6
7
8
9
10
11
12
Homework
Due: Wed. Dec. 2nd
4.1 page 158
 17-24
4.2 page 163
 9-12
4.2
Definitions:
PRIME: a number is prime when it is only
divisible by itself and 1.
COMPOSITE: a number that is divisible by
more than one number.
Sometimes
a number
that
cannotbybemore
divisible
by any
When a number
can be
divisible
numbers
than
other
number
a “1” is called:
the number
“1”than
is called:
PRIME Composite
What numbers are
13
divisible by?
1 x 13
What numbers are
45
divisible by?
3,9 5
Is the number
19 Prime
or Composite
Prime
Is the number
49 Prime
or Composite
Composite
Is the number
75 Prime
or Composite
Composite
Is the number
17 Prime
or Composite
Prime
Is the number
27 Prime
or Composite
Composite
Is the number
63 Prime
or Composite
Composite
Whole numbers that are multiplied together to find
another number
(Product) are called FACTORS.
2x3=6
Factors
Product
We write the prime factorization for the following number
Using the TREE
First we
choose any
two factors
to begin
with, and
keep
going till it
PRIME’s
out.
METHOD.
36
12
3
3
4
2
2
2x2x3x3
We write the prime factorization for the following number
Using the LADDER
First we
start with
the
smallest
prime
number,
and keep
dividing
out till we
get a final
prime
number
METHOD.
36
2x2x3x3
We write the prime factorization for the following number.
54
54
2x3x3x3
#5) Write the prime factorization for the following number.
48
48
2x2x2x2x3
4
Or
2 x3
#6) Write the prime factorization for the following number.
20
20
2 x 2 x 5 Or
2
2 x5
#7) Write the prime factorization for the following number.
66
66
2 x 3 x 11
#8) Write the prime factorization for the following number.
34
34
2 x 17
Homework
4.2 page 163
Due: Friday December 4th
5-8 and
17-24