Download Primes, Factors, & Multiples NOtes

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Find the common factors of two or more numbers
Determine the greatest common factor (GCF) of two
or more numbers
Determine whether a number is prime, composite,
or neither.
Determine the prime factorization of a given
number
Write the prime factorization using exponents
Find the common multiples of two or more numbers
Determine the least common multiple (LCM) of two
or more numbers.

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
Calculations
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 100).
20 is a composite number, we repeat Step 1.
3. Since 5 is a prime number we circle it. 4 is
a composite number, we repeat Step 1.
4. Since all the numbers are broken into prime
factors, we use them to write the product.
5. Then we write the prime factorization in
exponential form (using exponents).
100
20
5
5
4
2
2
2x2x5x5
2² x 5²

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.
There are two different ways to find 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


Using Prime Factorization: Find the prime
factorizations of each number. Circle all the
common prime factors. Multiply the
common prime factors to get the GCF.
12
18
4
3
3
2 2
2² x 3
6
2
3
2 x 3²
GCF = 2 x 3 = 6
Museum employees are preparing an
exhibit of ancient coins. They have 49
copper coins and 35 silver coins to
arrange on the shelves. Each shelf will
have the same number of copper coins
and the same number of silver coins.
How many shelves will the employees
need for the exhibit?
7 shelves

Multiple: a product of that number and
another whole number.


Example:
The multiples of 8 - 8, 16, 24, 32, 40 …
Common Multiples

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, 53, 60, 66…
Least Common Multiple: the smallest
multiple that two number have in
common.
There are two different ways to find 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…

Using Prime Factorization: Find the prime
factorizations of each number. Write them
in exponential form. Take each number that
is used. If they are used more than once, use
the one with the biggest exponent. Multiply
the common prime factors to get the GCF.
10
12
2x5
5
2
3
4
2
2
LCM = 2² x 3 x 5 = 60
2² x 3
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)