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A number is a factor of another given number if the given number can be EXACTLY divided by it • e.g. 6 is a factor of 18 because 18 divided by 6 is 3 • Note that 3 is then also a factor of 18 A PRIME number is one which can be divided ONLY by itself and 1 • It has two factors • 1 is NOT a prime number – it has only 1 factor All integers (whole numbers) other than 1 and prime numbers, are called COMPOSITE numbers. Composite numbers have more than 2 factors. e.g. 6 is composite because it can be divided by 2 and 3 as well as 1 and 6 so the number 6 has four factors. The factors of 6 are 1, 2, 3 and 6. A list of the first 20 primes is: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, …… What is the next one? To find the prime factorisation of 24: • Since the first prime number is 2, see if 2 is a factor of 24 by division • It is, since 24 divided by 2 is exactly 12 • Now try to see if 2 is a factor of 12 – it is! • So we have 24 = 2 x 12 = 2 x (2 x 6) • Continue to divide the answer by 2 until it will not divide exactly then move on to the next prime number which is 3 etc until you get to 1 • Then 24 = 2 x 2 x 2 x 3 x 1 • Since 24 = 2 x 2 x 2 x 3 we have written 24 as a product of its prime factors • In shorthand or index notation • 24 is written as 23 × 3 • because there are 3 twos multiplied by one 3 • To use the TI-15 Explorer™ to find the prime factors of a number the calculator needs to be set up in the following way: – Press button to enter the Fraction Menu. The selection U n/d n/d is displayed. This lets you choose to display fractions results as mixed numbers (U n/d) or improper fractions (n/d). • Press the left and right arrow keys to move the underline to choose the display you want. • In this case, move the underline to n/d. • Press the down arrow , and move the underline to MAN. This lets you choose to simplify fractions manually (using the key). • Select . Enter the fraction • Press (Remember the top line is the numerator and the bottom line is the denominator) If is visible at the top of the screen then the fraction can be simplified further. Press . The simplified fraction is displayed. Press and if, for example, a 2 is shown, the fraction has been simplified by dividing both the numerator and denominator by 2. This tells you that 2 is a factor of 24. If is still visible, then further simplification can occur. Continue until you have recorded all the prime numbers and your fraction is now 1/1. • You should have recorded that the fraction 24/24 became 12/12 then 6/6 then 3/3 then 1/1… • The factors were 2, 2, 2 and 3 • So 24 = 2 x 2 x 2 x 3 = 23 × 3 • which is called the prime factorisation of 24 • To check if a number is a prime, check if any of the prime numbers smaller than the square root of that number are factors. If not then the number is a prime. • e.g. is 156 prime? – no, since it is an even number and there is only one even prime – that is 2! • Is 157 prime? The square root of 157 is a bit bigger than 12. Check if 2, 3, 5, 7, 11 are factors of 157……….?