Using Euclid’s division algorithm, find which of the following pairs of numbers are co-prime:
(i) 231, 396
(ii) 847, 2160
Solution:
(i) First we have to determine the HCF of each pair of numbers.
396 = 231 × 1 + 165
231 = 165 × 1 + 66
165 = 66 × 2 + 33
66 = 33 × 2 + 0
HCF = 33
Therefore, numbers are not co-prime
(ii) 2160 = 847 × 2 + 466
847 = 466 × 1 + 381
466 = 381 × 1 + 85
381 = 85 × 4 + 41
85 = 41 × 2 + 3
41 = 3 × 13 + 2
3 = 2 × 1 + 1
2 = 1 × 2 + 0.
HCF = 1.
Therefore, the numbers are co-prime
✦ Try This: Using Euclid’s division algorithm, find which of the following pairs of numbers are co-prime: 6 and 10
Let us consider two numbers 6 and 10.
The factors of 6 are 1, 2, 3, and 6.
The factors of 10 are 1, 2, 5, and 10.
Factors that are common to both 6 and 10 are 1 and 2.
HCF = 2.
Therefore, 6 and 10 are not co-prime numbers
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.3 Sample Problem 1
Using Euclid’s division algorithm, find which of the following pairs of numbers are co-prime: (i) 231, 396 (ii) 847, 2160
Summary:
The numbers 231 and 396 are not co-prime, numbers 847 and 2160 are co-prime numbers
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