You get 20 = 2 × 10Ħ3 cannot be divided by 2, so try the next number after 2, which is 3.Ģ1 can be divided by 3 once again to get 7, so 21 = 3 × 7. Start by dividing 40 by 2, you get 40 = 2 × 20ĭivide 20 by 2 again because 20 can be divided by 2. When a number is written as the product of primes number, we call the expressed product prime factorization.įor instance, do the prime factorization of 40 and 24. You only had to try dividing 301 by 7 numbers as opposed to trying all numbers from 1 to 301Įvery composite number can be written as the product of prime numbers. However, 7 can divide 301 since 301 ÷ 7 = 43Īs you see, the prime factor test made it easier to check if a 301 was prime. Therefore, the prime factors you can use to do your test are 2, 3, 5, 7, 11, 13, and 17Ģ, 3, 5, 11, 13, and 17 cannot divide 301 Just search for prime factors n of 301 such as n 2 ≤ 301 To test for prime factor of a number x, just search for prime factors n of x, such as n 2 ≤ x This will be very useful when the number is big. The prime factor test will help you quickly determine if a number is prime or not. We show you the process for all numbers from 1 to 50 After you are done, you should find 25 prime numbers. Circle 3 and cross out all multiples of 3, such as 6, 9, 12. Look for the next number after 2 that is prime. Then, circle the next number after 1 that is prime, which is 2 Cross out all the multiples of 2 until you get to 100, such as 2, 6, 8, 10, 12.
Visit this page to learn more about how to check. In each iteration, whether low is a prime number or not is checked, and the value of low is incremented by 1 until low is equal to high. In this program, the while loop is iterated ( high-low-1) times. Sieve's Algorithm: Make a list of all numbers from 1 to 100 Start by crossing out 1 because it is not prime. Enter two numbers (intervals): 20 50 Prime numbers between 20 and 50 are: 23 29 31 37 41 43 47. As a shortcut, you can use a method or algorithm called Sieve of Eratosthenes, named after a famous Greek mathematician. How many numbers less than 100 are prime? You can use the definition to test every single number. Notice also that 2 is the only number that is even and prime at the same time. According to the definition, a number must have at least 2 factors before it can be prime or composite. 1 is neither prime nor composite because it has only one factor.