Download Primes, Factors, & Multiples NOtes

We often need to know quickly if one
number is a factor of another number.
Knowing the following rules can make
your factoring tasks much easier.
A number is divisible by …

2, if it ends in an even number in the
ones place (0, 2, 4, 6, 8)
 Example: 558 because there is an 8 in the ones
place
A number is divisible by …

3, if the sum of its digits is divisible by 3
 Example: 81 because 8 + 1 = 9 and 9 is divisible by
3
A number is divisible by …

4, if the last 2 digits are divisible by 4
 Example: 124 because 24 is divisible by 4
A number is divisible by …

5, if the ones digit is a 0 or a 5
 Example: 1125 because there is a 5 in the ones
place
A number is divisible by …

6, if the number is divisible by 2 AND 3
 Example: 48
 There is an 8 in the ones place so it is divisible by 2
 8 + 4 = 12 and 12 is divisible by 3
A number is divisible by …

8, if the last 3 digits are divisible by 8
 Example:1240 because there is 240 is divisible by 8
A number is divisible by …

9, if the sum of the digits is divisible by 9
 Example: 468 because 4 + 6 + 8 = 18 and 18 is
divisible by 9
A number is divisible by …

10, if the number ends in zero
 Example: 50 because the number ends in zero

Common Factors: factors that two or
more numbers have in common.

Example: Find all the common factors of
10 and 20 by listing all the factors.
 10: 1, 2, 5, 10
 20: 1, 2, 4, 5, 10, 20

Greatest Common Factor (GCF): the
biggest factor that two numbers have
in common.
Finding the GCF of two or more
numbers.
Using a list: List all the factors of each
number. Circle the greatest common
factor that appears in the list.
12
18
1
12
1
18
2
6
2
9
3
4
3
6
12
1
2
3
42
12
6
4
1
2
3
6
96
42
21
14
7
1
2
3
4
6
8
96
48
32
24
16
12
Mr. Grover wants to make shelves for
his garage using an 18-foot board and a
36-foot board. He will cut the boards
to make shelves of the same length and
wants to use all of both boards. Find
the greatest possible length of each
shelf.
18 ft
The SGB reps are making spirit ribbons.
Blue ribbon comes in a 24 inch spool,
red ribbon comes in a 30 inch spool,
and gold ribbon comes in a 36 inch
spool. The SGB reps want to cut strips
of equal length, using the entire spool
of each ribbon. What is the length of
the greatest piece of ribbon that can
be cut from each spool?
6 inches

Multiple: a product of that number and
another whole number.


Example:
The multiples of 8 - 8, 16, 24, 32, 40 …
Common Multiples: multiples that two
or more numbers have in common.

Example: Find some common multiples of 4
and 6 by listing at least ten multiples
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66…
•
Least Common Multiple: the smallest
multiple that two numbers have in
common, excluding zero.
Finding the LCM of two or more
numbers.
Using a list: List about ten multiples of
each number. Circle the lowest common
multiple that appears in the list.
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…
12: 12, 24, 36, 48, 60, 72, 84, 96, 108…
6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66 …
8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 ….
12: 12, 24, 36, 48, 60, 72, 84, 96, 108…
Rod helped his mom plant a vegetable
garden. Rod planted a row every 30
minutes, and his mom planted a row
every 20 minutes. If they started
together, how long will it be before
they both finish a row at the same
time?
60 minutes (1 hour)
Three bike riders ride around a
circular path. The first rider circles
the path in 12 minutes, the second in
18 minutes, and the third in 24
minutes. If they all start at the
same place at the same time, and go
in the same direction, after how
many minutes will they meet at the
starting point?
72 minutes

Composite Number: a number that has
more than two factors.


Prime Number: a number that only has
two factors; one and itself.


Example: 4, 28, 100
Example: 5, 29, 101
Primes less than 40:
2
3
5
7
11 13 17 19 23 29 31 37


Two numbers that are neither prime
nor composite: 0 and 1 .
Prime Factorization: writing a number
as a product of its prime factors.


Example: 30 = 2 x 3 x 5
You find the prime factorization of a
number by making a factor tree.
STEPS
1. Break the number down into two of its
factors, using a factor tree.
2. Since 5 is a prime number we circle it (this
means it is one of the prime factors of 150).
30 is a composite number, we repeat Step 1.
3. Since 5 is a prime number we circle it. 6 is
a composite number, we repeat Step 1.
4. Since both 2 and 3 are prime we circle them.
5. Since all the numbers are broken into prime
factors, we use them to write the product.
6. Then we write the prime factorization in
exponential form (using exponents).
Calculations