Prime Numbers and Prime Numbers and Prime FactorizationPrime Factorization

Developed by Kira Shank, M.EdDeveloped by Kira Shank, M.Ed

What you will learn….What you will learn….

How to find prime numbersHow to find prime numbers

How to find prime factors using prime How to find prime factors using prime factorizationfactorization

ExplanationExplanation Prime number Prime number – an integer larger than 1 that has only two – an integer larger than 1 that has only two

factors (1 and itself). There are exactly two factors. factors (1 and itself). There are exactly two factors.

1 is not a prime number because it only has 1 factor1 is not a prime number because it only has 1 factor

Prime FactorizationPrime Factorization – to find which prime numbers can be – to find which prime numbers can be multiplied together to make the original numbermultiplied together to make the original number

To find the prime factors of a number, a factor tree can be used.To find the prime factors of a number, a factor tree can be used.

Break down all factors until they are Break down all factors until they are only prime numbersonly prime numbers..

Worked ExamplesWorked Examples

Which of these numbers are prime numbers?Which of these numbers are prime numbers?

4, 11, 32, 614, 11, 32, 61

4 – not prime - factors are 1, 2, 44 – not prime - factors are 1, 2, 4

11 – prime – factors are 1, 1111 – prime – factors are 1, 11

32 – not prime – factors are 1, 2, 4, 8, 16, 3232 – not prime – factors are 1, 2, 4, 8, 16, 32

61 – prime – factors are 1, 6161 – prime – factors are 1, 61

Practice ProblemsPractice Problems

Which of these numbers are prime Which of these numbers are prime numbers? Explain or show your work. numbers? Explain or show your work.

5, 8, 20, 375, 8, 20, 37

SolutionsSolutions

5: 5: PrimePrime – factors are 1, 5 – factors are 1, 5

8: 8: Not PrimeNot Prime – factors are 1, 2, 4, 8 – factors are 1, 2, 4, 8

20: 20: Not PrimeNot Prime – factors 1, 2, 4, 5, 10, 20 – factors 1, 2, 4, 5, 10, 20

37: 37: PrimePrime – factors are 1, 37 – factors are 1, 37

Worked ExamplesWorked Examples

Prime Factorization for a given number can be figured out using a Prime Factorization for a given number can be figured out using a factor tree. factor tree.

What is the prime factorization of 24?What is the prime factorization of 24?

Therefore, 2*2*2*3 is the prime factorization 24. Therefore, 2*2*2*3 is the prime factorization 24.

24

6 4

2 22 3

Worked ExamplesWorked Examples

What is the prime factorization of 32?What is the prime factorization of 32?

Therefore, 2*2*2*2*2 is the prime factorization for 32. Therefore, 2*2*2*2*2 is the prime factorization for 32.

32

8 4

2 24 2

2 2

Practice ProblemsPractice Problems

What is the prime factorization of the following What is the prime factorization of the following numbers?numbers?

1414

5656

100100

SolutionsSolutions

What is the prime factorization of 14?What is the prime factorization of 14?

Therefore, 2*7 is the prime factorization for 14. Therefore, 2*7 is the prime factorization for 14.

14

2 7

SolutionsSolutions

What is the prime factorization of 56?What is the prime factorization of 56?

Therefore, 2*2*2*7 is the prime factorization for 56.Therefore, 2*2*2*7 is the prime factorization for 56.

56

8 7

4 2

2 2

SolutionsSolutions

What is the prime factorization of 100?What is the prime factorization of 100?

Therefore, 2*2*5*5 is the prime factorization for 100.Therefore, 2*2*5*5 is the prime factorization for 100.

100

10 10

2 52 5

Wrapping UpWrapping Up

A prime number is an integer larger than one A prime number is an integer larger than one that has exactly two factors.that has exactly two factors.

To find the prime factorization of a number, To find the prime factorization of a number, you must factor the number to all prime you must factor the number to all prime numbers. numbers.

The best way to do this is to use a factor tree. The best way to do this is to use a factor tree.