Transcript Prime Numbers and Prime Factorization

Prime Numbers and
Prime Factorization
Developed by Kira Shank, M.Ed
What you will learn….
How to find prime numbers
How to find prime factors using prime
factorization
Explanation

Prime number – an integer larger than 1 that has only two
factors (1 and itself).

1 is not a prime number because it only has 1 factor

Prime Factorization – to identify the set of prime factors that are
multiplied together to make the number

To find the prime factors of a number, a factor tree can be used.

Break down all factors until they are only prime numbers.
Worked Examples
Which of these numbers are prime numbers?
4, 11, 32, 61
4 – not prime - factors are 1, 2, 4
11 – prime – factors are only 1 and11
32 – not prime – factors are 1, 2, 4, 8, 16, 32
61 – prime – factors are only 1 and 61
Practice Problems
Which of these numbers are prime
numbers? Explain or show your work.
5, 8, 20, 37
Solutions
5:
Prime – factors are only 1 and 5
8:
Not Prime – factors are 1, 2, 4, 8
20:
Not Prime – factors 1, 2, 4, 5, 10, 20
37:
Prime – factors are only 1 and 37
Worked Examples
Prime Factorization for a given number can
be figured out using a factor tree.
What is the prime factorization of 24?
24
6
2
4
32
2
Worked Examples
What is the prime factorization of 32?
32
8
4
2
4
22
2
2
Practice Problems
What is the prime factorization of the
following numbers?
14
56
100
Solutions
What is the prime factorization of 14?
14
2
7
Therefore, 2*7 is the prime factorization for
14.
Solutions
What is the prime factorization of 56?
56
8
4
2
Therefore,
7
2
2
2*2*2*7 is the prime
factorization for 56.
 Written in exponent form: 23 * 7
Solutions
What is the prime factorization of 100?
100
10 10
2
Therefore,
52
5
2*2*5*5 is the prime
factorization for 100.
Written in exponent form: 22 * 52
Wrapping Up
A prime number is an integer larger than
one that has only two factors.
To find the prime factorization of a number,
you must factor the number to all prime
numbers.
The best way to do this is to use a factor
tree.