Download 1.9 Factor Strings and Prime Factorizations

1.9 Factor Strings and Prime
Factorizations
√ to review name-collection boxes
√ to represent numbers as products of factors (factor
strings) and as products of prime factors (prime
factorizations)
Math Message
8 + 8 and 4 x 4 are two names for the number
16. Write at least five other names for 16.
48/3
32/2
2x8
9+7
2
4
24 15 + 1
2 + 2 +2 +2+2+2+2+2
6 + 10
A factor
string is a name for a number written
as a product of at least two factors that are greater
than 1. In a factor string, the number 1 may not be
used as a factor.
Here are the factor strings for 30.
2 x 15
3 x 10
5x6
2x3x5
How do you do it?
Start with factor strings with only two factors.
List them all.
2 x 15
3 x 10
5x6
Take a factor pair and see if one of the numbers can
be made in to another factor pair.
2 x 15 = 2 x 3 x5
Keep trying to see if you can make a different
combination. (no turnarounds)
Find factor strings for 24.
Number
Factor String
Length
24
6x4
2
24
8x3
2
24
12 x 2
2
24
2x2x6
3
24
2x2x3x2
4
24
4x2x3
3
The prime factorization of 24 is 2 x 2 x 2 x 3.
Vocabulary
Name-Collection Box
A diagram that is used for writing equivalent names for
a number.
Factor String
A number written as a product of at least two wholenumber factors.
Example A factor string for the number 24 is 2 x 3 x
4. This factor string has three factors, so its length is 3.
The number 1 is never part of a factor string.
Prime Factorization
A whole number expressed as a product of prime
factors. Every whole number greater than 1 has a
unique prime factorization.
Example
x 3.
The prime factorization of 24 is 2 x 2 x 2
Length of Factor String
The number of factors a factor string has is its length.
Example
Another factor string for 24 is 3 x 8. This
factor string has two factors, so its length is 2.