Question

Which of the following numbers can be expressed as the product of $3$ different integers greater than $1$?
$I.24$
$II.27$
$III.48$

• A. $I$ and $III$ only
• B. $I$ and $II$ only
• C. $I,II$ and $III$
• D. $I$ only
• E. $III$ only

Answer 1

Answer: (A)

$I$ and $III$ only

We first write the three numbers using power of prime numbers as follows:

$24=2^3\times 3$

$27=3^3$

$48=2^4\times 3$

We now write if possible each of given numbers as the product of $3$ different integers

$24=2\times 4\times 3$

$27=3\times 9$ (not possible with three different integers greater than 1)

$48=2\times 8\times 3$

Hence $24$ and $48$ can be expressed as the product of $3$ different integers greater than $1$.

III