In 300 BC..A Greek Mathematician said: Let’s test his statement!! Euclid Greek Mathematician ανψ ιντεγερ γρεατερ τηαν 1 ξαν βε ωριττεν ας α προδυξτι οφ πριμε νυμβερς. Any whole number greater than 1 can be written as a product of prime numbers. Give an example with 4 = 2 x 2 and 10 = 5 x 2 so that students understand what they need to do. Let’s test his statement!!

All numbers can be made from primes 15 = 3 x 5 52 = 2 x 2 x 13 1000 = 2 x 2 x 2 x 5 x 5 x 5 123,456,789 = 3 x 3 x 3803 x 3607 2 3 5 Primes are the building blocks for all numbers

L.O. To be able to express a number as a Product of its Prime Factors By the end of the lesson, we will be able to: understand that any non-prime number can be written as a product of prime factors draw a factor tree use the factor tree to find the product of prime factors write this product in index form

How do we Find Prime Factors? Draw out the factor tree Split 18 into a pair of factors 18 2 9 2 is prime, so this branch is done 2 Split 9 into a pair of factors 3 3 18 = 2 x 3 x 3 Index Form! 18 = 2 x 32

How do we Find Prime Factors? Draw out the factor tree Split 30 into a pair of factors 30 3 10 3 is prime, so this branch is done 3 Split 10 into a pair of factors 5 2 5 2 30 = 3 x 5 x 2

How do we Find Prime Factors? Draw out the factor tree Split 45 into a pair of factors 45 5 9 5 is prime, so this branch is done 5 Split 9 into a pair of factors 3 3 45 = 5 x 3 x 3 Index Form! 45 = 5 x 32

Product of Prime Factors Draw out the factor tree Split 24 into a pair of factors 24 3 8 3 is prime, so this branch is done 3 Split 8 into a pair of factors 2 4 2 24 = 3 x 2 x 2 x 2 2 2 2 2 24 = 3 x 23

Product of Prime Factors Draw out the factor tree Split 24 into a pair of factors 24 4 6 Split 6 into a pair of factors 2 3 2 2 2 2 2 3 24 = 2 x 2 x 2 x 3 24 = 23 x 3

Product of Prime Factors Draw out the factor tree Split 24 into a pair of factors 24 2 12 2 is prime, so this branch is done 2 Split 12 into a pair of factors 2 6 2 24 = 2 x 2 x 2 x 3 2 2 3 3 24 = 23 x 3

A student has drawn the factor tree for 20. How would you help them identify their mistake? 2 x 2 x 5 c 2 x 5 2 10

Peer Assessment Plenary On your mini-whiteboards, prepare work of a student who got stuck to find the product of prime factors Swap whiteboards and correct the work to help the struggling student Re-swap and discuss the corrections with your partner

Homework: Draw Factor Tree for each STP 7 Pg 51 Exercise 4g No.s 2-8

PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … PRIME FACTOR TREES HW Pg 51 Ex 4g No. 2-8 Find the product of prime factors for the following numbers: (2) 28 (3) 63 9 7 7 4 3 3 2 2 ANSWER = 3 x 3 x 7 ANSWER = 7 x 2 x 2 𝟕× 𝟐 𝟐 = 𝟑 𝟐 ×𝟕 = 13

PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … PRIME FACTOR TREES HW Pg 51 Ex 4g No. 2-8 Find the product of prime factors for the following numbers: (4) 72 (5) 136 68 2 8 9 2 34 4 2 3 3 2 2 2 17 ANSWER = 2 x 2 x 2 x 17 ANSWER = 2 x 2 x 2 x 3 x 3 = 𝟐 𝟑 ×𝟏𝟕 = 𝟐 𝟑 × 𝟑 𝟐 14

PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … PRIME FACTOR TREES HW Pg 51 Ex 4g No. 2-8 Find the product of prime factors for the following numbers: (6) 84 (7) 216 36 6 4 21 9 4 3 2 2 2 7 3 2 2 3 3 ANSWER = 3 x 3 x 3 x 2 x 2 x 2 ANSWER = 2 x 2 x 7 x 3 𝟐 𝟐 ×𝟕×𝟑 = 𝟑 𝟑 × 𝟐 𝟑 = 15

PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … PRIME FACTOR TREES HW Pg 51 Ex 4g No. 2-8 Find the product of prime factors for the following numbers: 528 (8) 66 8 2 4 6 11 2 2 2 3 ANSWER = 2 x 2 x 2 x 2 x 3 x 11 = 𝟐 𝟒 ×𝟑×𝟏𝟏 16