Vocabulary

Product – An answer to a multiplication problem.

7 x 8 = 56

Product

Vocabulary

Factor – a number that is multiplied by another to give a product.

7 x 8 = 56

Factors

Vocabulary

Factor – a number that divides evenly into another.

56 ÷ 8 = 7

Factor

VocabularyPrime Number – a number that has only two factors, 1 and itself.

55 is prime because the only

numbersthat will divide into it evenly

are 1 and 5.

Prime Numbers:Eratosthenes’s

Sieve

Eratosthenes(ehr-uh-TAHS-thuh-neez)

Eratosthenes was a librarian from

Alexandria, Egypt in 200 B.C.E Note: every book was a scroll.

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.

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.

Hundreds Chart

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

100999897969594939291

90898887868584838281

80797877767574737271

70696867666564636261

60595857565554535251

50494847464544434241

40393837363534333231

30292827262524232221

20191817161514131211

10987654321

1 – Cross out 1; it is not prime.2 – Leave 2; cross out multiples of 23– Leave 3; cross out multiples of 34– Leave 5; cross out multiples of 55– Leave 7; cross out multiples of 7All the numbers left are prime!

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

Factors, Primes, & Composite Numbers

Vocabulary

Composite number – a number that has more than two factors.

8The factors of 8 are 1, 2, 4,

8

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.

1 is the Loneliest Number

One is not a prime nor a composite number.

It is not primebecause it

doesnot have exactly

two differentfactors.

It is not compositebecause it

doesnot have morethan 2 factors.

Definition Prime Factorization – A way to write a composite number as the product of prime factors.

2 x 2 x 3 = 12or

2 x 3 = 122

How to Do Prime Factorization Using a Factor Tree

Step 1: Begin with a composite number.Step 2: Find two factors that can be multiplied to make that numberStep 3: continue finding factors until all are prime.

364 9

2 2 3 3

Step 4: rewrite using exponents.

x x =36

2 3x2 2= 36

x

Prime Factorization

There is More Than One Way…

2 3

36

4 9

2 3

2 3x2 2

=36Prime Factorization

3

2

36

2 18

3

9 3 2

36

6 6

2 3

…but the prime factorization will always be the same.

How to Do Prime Factorization Using a Factor Tree

Step 1: Begin with a composite number.Step 2: Find two factors that can be multiplied to make that numberStep 3: continue finding factors until all are prime.

546 9

2 3 3 3

Step 4: rewrite using exponents.

x x =54

2 3x 3= 54

x

Prime Factorization

How to Do Prime Factorization Using a Factor Tree

Step 1: Begin with a composite number.Step 2: Find two factors that can be multiplied to make that numberStep 3: continue finding factors until all are prime.

486 8

2 3 22 2Step 4: rewrite

using exponents.

2 3x4 =48

4

Prime Factorization