1. Prime and
Composite Numbers

2. Vocabulary Product Product – An answer to a multiplication problem.
7 x 8 = 56
Product

3. Vocabulary
Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors

4. Vocabulary
Factor – a number that divides evenly into another.
56 ÷ 8 = 7
Factor

5. 5 Vocabulary 5 is prime because the only numbers
Prime Number – a number that has only two factors, 1 and itself. 5
5 is prime because the only numbers
that will divide into it evenly are 1 and 5.

6. Prime Numbers: Eratosthenes’s Sieve

7. Eratosthenes (ehr-uh-TAHS-thuh-neez)
Eratosthenes was a librarian from
Alexandria, Egypt in 200 B.C.E
Note: every book was a scroll.

8. Eratosthenes (ehr-uh-TAHS-thuh-neez)
Eratosthenes was a Greek mathematician, astronomer, and geographer.
He invented a method for finding prime numbers that is still used today.
This method is called Eratosthenes’ Sieve.

9. Eratosthenes’ Sieve
A sieve has holes in it and is used to filter out the liquid.
Eratosthenes’s sieve filters out numbers to find the prime numbers.

10. Hundreds Chart
On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

11. All the numbers left are prime!
4– Leave 5; cross out multiples of 5
2 – Leave 2; cross out multiples of 2
3– Leave 3; cross out multiples of 3
5– Leave 7; cross out multiples of 7
All the numbers left are prime!
1 – Cross out 1; it is not prime. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

12. The Prime Numbers from 1 to 100 are as follows:
2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73,
79, 83, 89, 97

13. Factors, Primes, & Composite Numbers

14. 8 Vocabulary The factors of 8 are 1, 2, 4, 8
Composite number – a number that has more than two factors. 8
The factors of 8 are 1, 2, 4, 8

15. Examples of Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15
Special Note:
Every whole number from 2 on is
either composite or prime.

16. 1 is the Loneliest Number
It is not prime
because it does
not have exactly
two different
factors.
It is not
composite
because it does
not have more
than 2 factors.
One is not a prime nor
a composite number.

17. Definition
Prime Factorization – A way to write a composite number as the product of prime factors.
2 x 2 x 3 = 12 or 2
2 x 3 = 12

18. How to Do Prime Factorization Using a Factor Tree
Step 1: Begin with a composite number. 36
Step 2: Find two factors that can be multiplied to make that number 4 9 2 3 2 3
=36 x x x
Step 3: continue finding factors until all are prime.
Prime Factorization 2 2 2 x 3
= 36
Step 4: rewrite using exponents.

19. There is More Than One Way…36 36 36 4 9 2 18 6 6 2 2 3 3 2 9 2 3 2 3 3 3
…but the prime factorization will always be the same.
Prime Factorization 2 2 x 2 3
=36

20. How to Do Prime Factorization Using a Factor Tree
Step 1: Begin with a composite number. 54
Step 2: Find two factors that can be multiplied to make that number 6 9 x 2 x x 3 3
=54 3
Step 3: continue finding factors until all are prime.
Prime Factorization 3 2 x 3
= 54
Step 4: rewrite using exponents.

21. How to Do Prime Factorization Using a Factor Tree
Step 1: Begin with a composite number. 48
Step 2: Find two factors that can be multiplied to make that number 6 8 4 2 3 2
Step 3: continue finding factors until all are prime.
Prime Factorization 4 x 2 2 3
=48 2
Step 4: rewrite using exponents.