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Which of the following expression(s) is/are true?

I. 337 is a prime number.

II. The number 12 has 6 positive factors.

III. 32724 is completely divisible by 9.

a

Only I

b

Only I and II

c

Only II and III

d

All expressions are true

Answer : Option D
Explanation :

I. 33718\sqrt{337} \approx 18

Number 337 is not divisible by 2,3,5,7,11,132,3,5,7,11,13 and 17(<18)17(<18).

Hence, 337 is a prime number.

II. 12 = 2 × 2 × 3 = 2² × 3

∴ Number of factors of 12 = (2 + 1) (1 + 1) = 3 × 2 = 6

III. 32724 ⇒ 3 + 2 + 7 + 2 + 4 = 18

32724 ÷ 9 = 3636

Here, 18 is divisible by 9.

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