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PRODUCT OF PRIME FACTORS Product of Prime Factors ANY whole number can be broken down and written as a Product of Prime Factors What is a PRIME FACTOR ? A PRIME FACTOR is a FACTOR that is also a PRIME NUMBER. Lets do a factor example ... The Prime Factors of a Number Example Question Express 108 as a Product of Prime Factors We use the “Factor Tree” Method 108 12 4 2 3 2 9 3 3 Prime Factors are the “fruits” of our “tree” ..... Product of Prime Factors ....from the previous page we obtained 2, 2, 3, 3, 3 as PRIME FACTORS of 108 So 108 = 2x2x3x3x3 108 = 22 x 33 Product Of Prime Factor Questions 1) Express 240 as a Product of Prime Factors 2) Express 150 as a Product of Prime Factors 3) Express 256 as a Product of Prime Factors 4) What do you think Highest Common Factor and Lowest Common Multiple mean ? Product of Prime Factors Answers 1) Express 240 as a Product of Prime Factors 2x2x2x2x3x5 = 24 x 3 x 5 2) Express 150 as a Product of Prime Factors 2x3x5x5 = 2 x 3 x 52 3) Express 256 as a Product of Prime Factors 28 4) What do you think Highest Common Factor and Lowest Common Multiple mean ? ....... HCF Highest Common Factor (HCF) is the biggest number that will divide into both of two or all of more numbers ... The HCF of 240 (2x2x2x2x3x5) and 150 (2x3x5x5) is 2x3x5 ..... Why ? Because 2x3x5 are the numbers in both lists, So HCF of 240 and 150 = 30 HCF Questions The following numbers have already been broken down into Products of Prime Factors, find the Highest Common Factors ... 1) 2x2x2x3x3x5 and 2x3x3x5x7 2) 3x3x3x5x7x7 and 2x2x3x3x7x11 3) 5x5x7x11x11 and 2x5x7x11x13 HCF Answers The following numbers have already been broken down into Products of Prime Factors, find the Highest Common Factors ... 1) 2x2x2x3x3x5 and 2x3x3x5x7 2x3x3x5 1) 3x3x3x5x7x7 and 2x2x3x3x7x11 3x3x7 1) 5x5x7x11x11 and 2x5x7x11x13 5x7x11 LCM Lowest Common Multiple (LCM) is the lowest number that both numbers are FACTORS of .. 1) Find the LCM of i) 2x2x3x5 and ii) 2x5x7 Do the minimum possible to make both products the same .. i) 2x2x3x5x7 ii) 2x5x7x2x3 LCM = 420 LCM Questions Find the Lowest Common Multiples ... 1) 2x3x5x7 and 2x2x7 2) 2x3x3x5x7 and 3x11 3) 2x2x2x13 and 3x11x13 4) 2x7 and 3x19 LCM Answers Find the Lowest Common Multiples ... 1) 2x3x5x7 and 2x2x7 2x3x5x7x2 2) 2x3x3x5x7 and 3x11 2x3x3x5x7x11 3) 2x2x2x13 and 3x11x13 2x2x2x13x3x11 4) 2x7 and 3x19 2x7x3x19 Summary • Any whole number can be broken down into a Product of Prime Factors. • We use the “Factor Tree” method where the Prime Factors are our “fruit”. • Products of Prime Factors can be used to find Highest Common Factors and Lowest Common Multiples.