Transcript PRIME NUMBERS

INTRODUCTION TO PRIME
NUMBERS
A Reminder of Two Important Words
Before we start to investigate Prime Numbers
lets remind ourselves of Factors and Multiples
1) Factor – A Factor is the proper name for any
number that will divide into another e.g. 6 is a
factor of 36, 5 is a factor of 30 etc.....
2) Multiple – A Multiple is the proper name
for the result of a multiplication e.g. 36 is a
multiple of 6, 30 is a multiple of 5 etc ........
Prime Numbers
1. Prime Numbers can only be divided by
themselves and 1.
2. 1 itself is not a Prime Number
3. Any number can be broken down to a
Product of Prime Factors (Prime Number
Decomposition) .. See later work
Prime Numbers Up To 100 ....
Remember ! You won’t find Prime Numbers in
any times table. (1 is NOT Prime)
2, 3, 5, 7, 11 .........are all Prime Numbers
Can you find other Prime Numbers up to 100 ?
Prime Numbers Up To 100 ....
Remember ! You won’t find Prime Numbers in
any times table. (1 is NOT Prime)
2, 3, 5, 7, 11 .........are all Prime Numbers
Can you find other Prime Numbers up to 100 ?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
77, 79, 83, 89, 91, 97
How To Find A Prime Number....
A Simple Method
1) It must end in either 1, 3, 7 or 9
2) Find the square root of the number and
make sure that the Primes below the square
root won’t divide into it.
e.g. Is 241 a prime number ? 1, 3, 7 or 9 OK !
241 = 15.52.. x 15.52.. Primes less than 15 are 2,
3, 5, 7, 11, 13 .. NONE divide 241, 241 is Prime !
Prime Number Exercise
1) Write down all the Prime Numbers up to 50
2) What is a i) Factor ii) Multiple
3) Are the following numbers Prime ?
i) 119 ii) 241 iii) 163 iv) 1872
Remember: Does it end in 1, 3, 7 or 9, Does it
divide by primes below square root.....
Prime Number Exercise Answers
1) Write down all the Prime Numbers up to 50
2,3,5,7,11,13,17,19,23,29,31,37,41,43, 47
2) What is a i) Factor ii) Multiple
i) A dividing number ii) result of multiplication
3) Are the following numbers Prime ?
i) 119 no (7) ii) 241 yes iii) 163 yes iv) 1872 no
Remember: Does it end in 1, 3, 7 or 9, Does it
divide by primes below square root.....
Summary
• A Prime Number can only be divided by itself
and 1.
• ANY whole number can be broken down into a
multiplication (product) of Prime Factors ....
see later work
• 1 is NOT a Prime Number