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10b Factors and multiples Work out each of these. a 43 b ⫺25 c 104 example example 10a 10a2 Cubes, cube roots and indices a 43 ⫽ 4 ⫻ 4 ⫻ 4 ⫽ 64 b ⫺25 ⫽ ⫺2 ⫻ ⫺2 ⫻ ⫺2 ⫻ ⫺2 ⫻ ⫺2 ⫽ ⫺32 c 104 ⫽ 10 ⫻ 10 ⫻ 10 ⫻ 10 ⫽ 10 000 1 Without using a calculator, write the value of these. 3 a 33 b 53 c 34 d √8 2 Use your calculator to find each of these. 3 a 83 b 4.53 c ⫺23 d √3375 3 e √64 3 e √⫺64 3 a Copy and complete this sequence for three more lines. 13 ⫽ 12 13 ⫹ 23 ⫽ 32 13 ⫹ 23 ⫹ 33 ⫽ 62 3 1 ⫹ 23 ⫹ 33 ⫹ 43 ⫽ 102 b What is the name of the sequence that begins 1, 3, 6, 10, …? 4 There are two numbers between 1 and 100 that are both a square number and a cube number. One of them is 1. What is the other? 5 Use your calculator to find each of these. a 25 b 63 c 34 d 106 e 255 Find the LCM of 6 and 14. List some multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, … List some multiples of 14: 14, 28, 42, 56, 70, … Choose the smallest number that appears in both lists. The LCM of 6 and 14 is 42. 1 Write the first eight multiples of these numbers. a 3 b 5 c 8 d 12 e 25 2 Using your answers to question 1 to help you, find the lowest common multiple (LCM) of these pairs of numbers. a 3 and 5 b 3 and 8 c 8 and 12 d 5 and 25 3 This table shows all the products that make up the numbers 12 and 15. Copy and complete the table and find the highest common factor (HCF) of 12 and 15. Number Products 12 1 ⫻ 12 2⫻6 15 1 ⫻ 15 3⫻5 Factors 3⫻4 4 Find the HCF of these pairs of numbers. a 8 and 10 b 6 and 15 c 18 and 30 d 7 and 29 e What can you say about the numbers in part d? 5 True or false? Explain your answers. a The smallest factor of any number is 1. b All numbers except 1 have an even number of factors. c Any multiple of 8 is also a multiple of 2 and 4. 58 Algebra Cubes, cube roots and indices Algebra Factors and multiples 59