1.3 Square roots and cube roots

1 Integers

1.1 Factors, multiples and primes

Key words factor tree highest common factor (HCF) lowest common multiple (LCM) prime factor Exercise 1.1 Focus 1 a Draw a factor tree for 250 that starts with 2 × 125. b Can you draw a different factor tree for 250 that starts with 2 × 125? Give a reason for your answer. c Draw a factor tree for 250 that starts with 25 × 10. d Write 250 as a product of its prime factors. 2 a Draw a factor tree for 300. b Draw a different factor tree for 300. c Write 300 as a product of prime numbers. 3 a Write as a product of prime numbers i 6 ii 30 iii 210 b What is the next number in this sequence? Why? 4 Work out a 2 × 3 × 7 b 22 × 32 × 72 c 23 × 33 × 73 5 a Draw a factor tree for 8712. b Write 8712 as a product of prime numbers. 6 Write each of these numbers as a product of its prime factors. a 96 b 97 c 98 d 99 Practice© Cambridge University Press 2022 7 Write as a product of prime numbers a 70 b 702 c 703 8 a Write each square number as a product of its prime factors. i 9 ii 36 iii 81 iv 144 v 225 vi 576 vii 625 viii 2401