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0 Had a look 0 Nearly there Nailed it! 0 NUMBER I A B C D --I-"-h...- F'" ,r:l'("IRC'>·-7i,f · a nomb·e r are any numbers that divide Into It exactly. PRIME NUMBER has exactly two factors. It can only be. divided by I and Itself. 84 a number IS a factor of another number AND It Isa prime number then It IS .. ca~~e~ at:~~~Ep~~~~7a~o~~:use a ~ 84 = 2 X 2 X 3 . = 2,'2 X 3 X 7~_.. Remember to circle the prime fact"rs as ..------- _ ~~~e~od;~:~~ ~a~ter. .... ..... ~ ~2 8 ('0 ~® + _. _..._ Reniembe-'; to put In the multiplication signs. 15 callega. PROPUCT_of.E'RIME FACTOR5 . ~- .. __ ._.._.. . ThiS .. _ - - - - - The lowesf commonmultiple (LCMfOf t wo . numbers _ls_the_LOWE5T NUMBER-that .ls a . MULTIPLE of both numbers. The highest common factor (HCF) of two _J--I-rlurrlbers IS the HIGHE5T~NUMBERthat IS a FACTOR of both numbers. -------------------------------------- ~- When draWing a factor tree, make sure you t;continue until every branch ends with a prime number. It doesn't matter which factor pairs .. you choose for each branch. At the end, don't ~ forget to write out the product of primes. Worked. example (a) Express 108 as a product of its prime factors. 108 Everything In red IS part of the <::-----1--< answer. ~ o Check ItI 54 ~...I- ~ G ·. f 9 0~Xj)~ (b) Find the highest common factor (HCF) of 108 and 24 1 ! ~ "-.___.--"'--"--- . ..!'_~.~..-'_.__ , --- = 108 ./ _.- _. ...-. _ .._-_ .. - ...-...___-_.. ---' .... _ _ To find the HCF Circle all the pnme numbers which are common to both products of pnme factors. 2 appears tWice In both products so you have to Circle It tWice. Multiply the Circled numbers together to ~ find the HCF. l L ------------_..,f r· To find the LCM multiply the HCF by the (c) Find the lowest common mUltiple (LCM) of 108 and 24 LCM = 12 X 3 X 3 X 2 = 21G - . ~ 108 = ® X ® X @ X 3 X 3 24. =®X®X 2 xC) HCF IS 2 X 2 X 3 = 12 -- --- ----- -- ----- _ t 108 = 2 X 2 X 3 X 3 X 3 = 2 2 X 3 3 ""'AM"._~""'_""'- 2 X 2 X3 X3 X3 numbers In both products that were not Circled In part (b). Alternatively, you can multiply 108 and 24 together and diVide by the HCF: 108 X 24 = 2592 2592 7 12 = 21G ...;;'- - Now try this (a) Express the following numbers as products of their prime factors. (i) 60 (ii) 96 (4 marks) - -~-----------------......... - edexceli!5 (b) Find the highest common factor (HCF) of 60 and 96 (1 mark) (c) Work out the lowest common multiple (LCM) of 60 and 96 (1 mark) 1