Mr O’Donovan Mathematics Room 306 Work hard Be nice

Circle as many prime numbers as you can remember. Is there a method for finding primes? Try to write a definition of a prime number underneath your grid.

Driving question What is a prime number and why are they important? Sunday, 24 February 2019 New topic: Number Title: Prime factors Challenge question How do know I have listed every factor? Driving question What is a prime number and why are they important? List factors in a systematic, logical way and identify prime and common factors Explain efficient strategies for ensuring all factors are listed Define and give examples of a prime number and prime factor

Worked Example: Prime Factors A factor is a number that divides into another number leaving no remainder. It is best to list factors in pairs. Example the factors of 24. A prime factor is a factor of a number that is also prime.

Factors and Multiples A prime number which divides into another number without leaving a remainder is called a prime factor of the number. Find the prime factors of the following: a b c d 16 20 24 25 2 2 and 5 2 and 3 5 e 28 f 36 g 49 h 23 2 and 7 2 and 3 7 23 i j k l 30 42 110 210 2, 3, and 5 2, 3 and 7 2, 5, and 11 2,3,5 and 7

Worked Example: Highest Common Factors The highest common factor (HCF) of two numbers is the largest factor they have in common. For example: Find the HCF of 24 and 40

What is the highest common factor of 12 and 20? Factors of 12 Factors of 20

Find the Highest Common Factor 15 and 20 15 and 60 12 and 22 12 and 66 39 and 52

How do I know if I have listed all the factors?

Co-Prime If a pair of numbers have a highest common factor of 1 then they are co-prime. So for example We can say “the numbers 5 and 6 are co-prime” or “5 is co-prime with 6” because the HCF of 5 and 6 is 1. Notice that the number 6 can be “co-prime” with 5 even though it is not prime itself!

Co-Prime Investigation Which of the factors of 120 are coprime (they have a highest common factor of 1)? When you think you have them all answer these: Are prime factors always coprime with each other? What is special about the consecutive factors of 120? How many times is the number 1 one of the coprime pair? Select a coprime pair, multiply them together and record the result. Repeat with a different coprime factor pair of 120. Do you notice anything about the sum and product of coprime factor pairs? Start with numbers other than 120. Does the same thing always happen? Convince yourself. Extension Work underneath Prime factors are always coprime with each other –Examples: 2 and 3, 2 and 5, 3 and 5. Consecutive numbers are always coprime – e.g. 1 and 2, 2 and 3, 3 and 4, 4 and 5. 1 is one of the coprime pairs 15 times (1 and another factor is always co-prime). So always number of factors -1

http://bit.do/ulam Taffic stats of hwk - http://bit.do/ulam-