# SIEVE OF ERATOSTHENES WORKSHEET

Question 1 : In the grid shown above, do the following :

(i) Circle the smallest number that is not already circled or crossed out.

(ii) Cross out all of the multiples of the number you circled in Step 1 except the circled number itself.

(iii) Repeat Steps 1 and 2 until every number on the grid is either circled or crossed out.

Question 2 :

Use Sieve of Eratosthenes method and find all the composite and prime numbers from 1 to 100.

Question 3 :

How many prime number are there from 1 to 100?

Question 4 :

How many prime numbers end with 5?

Question 5 :

How many prime numbers are even?

Question 6 :

Find the sum of the smallest and largest two-digit prime numbers.

Question 7 :

What is the difference between the smallest two-digit prime number and the smallest one-digit prime number?  Look at the grid in 1. Answer above.

From the Sieve of Eratosthenes, we observe that, the crossed-out numbers are composite and the colored numbers (encircled) are primes.

The total number of prime numbers from 1 to 100 is 25.

There is only one prime number that ends with 5 is 5.

There is only one prime number which is even, that is 2.

From the grid in 1. Answer,

the smallest two-digit prime number = 11

the largest two-digit prime number = 97

Sum of the smallest and largest two-digit prime numbers :

= 11 + 97

= 108

From the grid in 1. Answer,

the smallest two-digit prime number = 11

the smallest one-digit prime number = 2

Difference between the smallest two-digit prime number and the smallest one-digit prime number :

= 11 - 2

= 9

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