Co-prime Numbers

Transcript

Co-prime NumbersLet’s take two numbers 8 and 9 Other co-prime numbers can be 2, 3 5, 9 11, 15 Since only 1 is common factor ∴ 8 & 9 are co-prime Checking if co-prime Let’s check if 81 and 16 are co-prime Factors of 81 1 × 81 = 81 3 × 27 = 81 9 × 9 = 81 27 × 3 = 81 We stop as 3 & 27 have occurred earlier Factors of 81 are 1, 3, 9, 27, 81 Factors of 16 1 × 16 = 16 2 × 8 = 16 4 × 4 = 16 8 × 2 = 16 We stop here as 8 and 2 have occurred earlier Factors of 16 are 1, 2, 4, 8, 16 Check if 17 and 68 are coprime Since common factor is 1, They are co-prime numbers Factors of 17 1 × 17 = 17 17 × 1 = 17 We stop as 1 & 17 have occurred earlier So, factors of 17 are 1 and 17 Factors of 68 1 × 68 = 68 2 × 34 = 68 4 × 17 = 68 17 × 4 = 68 We stop as 17 and 4 have occurred earlier So factors of 68 are 1, 2, 4, 17, 34, 68 Example 1 (Page 116) Which of the following pairs of numbers are co-prime? (a) 18 and 35 Factors of 18 1 × 18 = 18 2 × 9 = 18 3 × 6 = 18 6 × 3 = 18 We stop here as 3 & 6 have occurred earlier So factors of 18 are 1, 2, 3, 6, 9, and 18 Factors of 35 1 × 35 = 35 5 × 7 = 35 7 × 5 = 35 We stop here as 7 and 5 have occurred earlier So factors of 35 are 1, 5, 7, 35 Factors of 35 1 × 35 = 35 5 × 7 = 35 7 × 5 = 35 We stop here as 7 and 5 have occurred earlier So factors of 35 are 1, 5, 7, 35