Question

which of the following pairs of numbers are co-prime numbers? a) 32,729 b) 130,39 c) 121,61 d) 54,936

Answer 1

♦ Co-Prime Numbers:
Two numbers whose HCF is 1 are called co-prime numbers.

In other words, two numbers which don't have any common factor (except 1) between them are called co-prime.

So, we just need to check the HCF of given numbers.

a) 32 and 729

32 = 2^5
729 = 3^6

Clearly, HCF = 1

So, 32 and 729 are co-prime.

b) 130 and 39

130 = 2×5×13
39 = 3×13

Here, HCF = 13

As HCF ≠ 1, 130 and 39 are not co-prime.

c) 121 and 61

121 = 11²
61 is prime

So, HCF = 1

Clearly, 121 and 61 are co-prime.

d) 54 and 936

(Shortcut: Here we see that both are divisible by 2. So HCF≠1. So they are not co-prime)

54 = 2×3³
936 = 2³ × 3² × 13

Here HCF = 2 × 3² = 18

As HCF ≠ 1, 54 and 936 are not co-prime.


→ So, numbers in pairs (a) and in (c) are co-prime.

Answer 2

Answer:

♦ Co-Prime Numbers:

Two numbers whose HCF is 1 are called co-prime numbers.

In other words, two numbers which don't have any common factor (except 1) between them are called co-prime.

So, we just need to check the HCF of given numbers.

a) 32 and 729

32 = 2^5

729 = 3^6

Clearly, HCF = 1

So, 32 and 729 are co-prime.

b) 130 and 39

130 = 2×5×13

39 = 3×13

Here, HCF = 13

As HCF ≠ 1, 130 and 39 are not co-prime.

c) 121 and 61

121 = 11²

61 is prime

So, HCF = 1

Clearly, 121 and 61 are co-prime.

d) 54 and 936

(Shortcut: Here we see that both are divisible by 2. So HCF≠1. So they are not co-prime)

54 = 2×3³

936 = 2³ × 3² × 13

Here HCF = 2 × 3² = 18

As HCF ≠ 1, 54 and 936 are not co-prime.

→ So, numbers in pairs (a) and in (c) are co-prime