




Last updated at July 9, 2025 by Teachoo
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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 Example 1 (Page 116) Which of the following pairs of numbers are co-prime? (b) 15 and 37 Factors of 15 1 × 15 = 15 3 × 5 = 15 5 × 3 = 15 We stop here as 5 & 3 have occurred earlier So factors of 15 are 1, 3, 5, 15 Factors of 37 1 × 37 = 37 37 × 1 = 37 We stop here as 37 and 1 have occurred earlier So factors of 37 are 1, 37 Since common factor is 1, They are co-prime numbers Example 1 (Page 116) Which of the following pairs of numbers are co-prime? (c) 30 and 415 Factors of 30 1 × 30 = 30 2 × 15 = 30 3 × 10 = 30 5 × 6 = 30 6 × 5 = 30 We stop as 6 & 5 have occurred earlier So factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30 Factors of 415 1 × 415 = 415 5 × 83 = 415 83 × 5 = 415 We stop here as 83 and 5 have occurred earlier So factors of 415 are 1, 5, 83, 415 So, common factors are 1, 5 Since common factors are other than 1, They are not co-prime numbers Example 1 (Page 116) Which of the following pairs of numbers are co-prime? (d) 17 and 69 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 69 1 × 69 = 69 3 × 23 = 69 23 × 3 = 69 We stop as 23 and 3 have occurred earlier So factors of 69 are 1, 3, 23, 69 Example 1 (Page 116) Which of the following pairs of numbers are co-prime? (f) 81 and 18 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 18 1 × 18 = 18 2 × 9 = 18 3 × 6 = 18 6 × 3 = 18 We stop here as 6 and 3 have occurred earlier Factors of 18 are 1, 2, 3, 6, 9, 18