FactorsAndMultiples

=Factors and Multiples= = =

The Sieve of Eratosthenes
Click here to see a picture of Eratosthenes:[|Eratosthenes]

I've got some questions for you to think about when doing the Sieve of Eratosthenes to find prime numbers. Q1. Which multiples form vertical lines? Why do you think these colums are shaded? Q2. Which multiples form slanted lines? Q3. Find two multiples that have similar patterns. Which multiples did you choose? Describe how the patterns are similar?

When checking whether a number, n, is prime, all we need to do is to check whether n can be divided by prime numbers up to square root of n.

Prime and Composite Numbers
What is a [|prime number]? What is the largest known prime number today? http://primes.utm.edu/largest.html

1 is a factor of every number. The number itself is also a factor of the numer.

Every composite number can be factored into a product of prime numbers in one and only one way. For example, 32 = 2x2x2x2x2.

We can use prime factorisation of numbers to find HCF and LCM. For example, 24 = 2x2x2x3 32 = 2x2x2x2x2 HCF (24,32) is 2x2x2 = 8 LCM (24,32) is 2x2x2x2x2x3 =96

If you use index notation to represent the prime factorisation, it may be easier to work out the HCF and LCM. To find HCF, for each common prime factor, choose the one with the lowest index and multiply them. To find LCM, for each prime factor, choose the one with the highest index and multiply them.


 * Try this website to find the prime factorisation of a number using a tree diagram:**
 * http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html?from=grade_g_3.html**