Sieve of Eratosthenes

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 the Sieve of Eratosthenes. Eratosthenes (ehr-uh-tahs-thuh-neez)

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

FACTOR A Factor is a number that is multiplied by another number to give the product. 7 x 8 = 56 Factors

FACTOR A Factor is the number that divides evenly into another. 56 ÷ 8 = 7 Factor

PRIME NUMBER A Prime Number is a number that has only two factors, itself and is prime because the only numbers that will divide into it evenly are 1 and 7.

Hundreds Chart I am going to give you a hundreds chart with the numbers from 1 to 100, with 10 numbers in each row. You are going to use the Sieve of Eratosthenes to discover the prime numbers between 1 and 100.

Hundreds Chart

– Cross out 1; it is NOT prime.

Hint For Next Step Remember all numbers divisible by 2 are even numbers. Remember they end in 0, 2, 4, 6, 8…

– Leave 2; Cross out multiples of 2

Hint For Next Step To find multiples of 3, add the digits of a number. If the sum divides evenly by 3 then the number is a multiple of Add the digits: = is divisible by 3 so 267 is a multiple of 3

– Leave 3; Cross out multiples of 3

Hint For the Next Step Remember the number 4 is a multiple of 2 a nd an even number. You don’t have to do multiples of 4 since you already crossed off multiples of 2.

To find the multiples of 5 look for numbers that end with the digit 0 and 5.5. Hint For the Next Step 385 is a multiple of 5 and 890 is a multiple of 5 because the last digit ends with 0 or 5.

– Leave 5; Cross out multiples of 5

Hint For the Next Step Remember a number is divisible by 6 if it is divisible by 2 and 3. Since you have already crossed out multiples of 2 and 3 then you have already done multiples of 6.

– Leave 7; Cross out multiples of 7

Hint For the Next Step Remember the number 8 is a multiple of 2, the number 9 is a multiple of 3, and the number 10 is a multiple of 2.2. What number do you think is next?

– Leave 11; Cross out multiples of 11

The leftover numbers are prime numbers.

Circle the rest of the primes on your chart.

The Prime Numbers from 1 to 100 are as follows: Write these down on the bottom of your paper: 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 A prime number is a number that has no factors other than 1 and itself. There are 25 prime numbers from 0 to 100. Check your list to make sure you have them all!

Composite numbers have more than 2 factors. PRIME FACTORIZATION is the unique set of prime numbers whose product equals a given number. Write the prime factorization for the following. 24 Factor Tree

Take Out Your Study Guide!!!

FACTOR A Factor is a number that is multiplied by another number to give the product. 7 x 8 = 56 Factors A Factor is the number that divides evenly into another number. 56 ÷ 8 = 7 Factor #3

Prime Numbers- A Prime number is a whole number with exactly 2 factors, one and itself. Example: 17, 3, 2, 11, 13, 5 Composite Numbers- A Composite number is a number that has more than two factors. Example: 9, 30, 64, 8, 40, 69 #4 Prime & Composite

Teacher Note : Use the next slide as a master. Make one copy for each student to use to do this interactive lesson on discovering prime numbers

Hundreds Chart