Question

The product of 2 consecutive natural numbers is 72. Find the numbers.

• A. 8,9
• B. -8, -9
• C. 36, 2
• D. 18, 4

Answer 1

The correct option is A

8,9

Let the smaller number be $x$. Then the larger number is $x+1$.

Their product is $x(x+1)$.

$\Rightarrow$ $x(x+1)=72$

$\Rightarrow$ $x^2+x-72=0$

$\Rightarrow$ $x^2+9x-8x-72=0$

$\Rightarrow$ $x(x+9)-8(x+9)=0$

$\Rightarrow$ $(x-8)(x+9)=0$

$\Rightarrow$ $x=8orx=-9$

Since the given numbers are natural numbers, we get $x=8$

Hence the two consecutive natural numbers are 8 and 9.