The product of two consecutive natural numbers is 12. The greater of the two numbers is:

The correct answer is 4.

Step 1: Understand the Problem

We are given that the product of two consecutive natural numbers is equal to 12. We need to find the greater of these two natural numbers.

Step 2: Formulate the Equation

Let the smaller natural number be represented by $x$.

Since the numbers are consecutive, the greater natural number will be $x+1$.

According to the problem statement, their product is 12:

$x(x+1)=12$

$x^2+x=12$

$x^2+x-12=0$

Step 3: Solve the Quadratic Equation

Factorize the quadratic equation by finding two numbers that multiply to -12 and add up to 1 (the coefficient of $x$):

The factors of -12 that sum to 1 are 4 and -3.

$(x+4)(x-3)=0$

This gives two possible values for $x$:

$x=-4$ or $x=3$

Step 4: Select the Valid Value

Since the question specifies that the numbers are natural numbers (positive integers starting from 1), we reject $x=-4$.

Therefore, the smaller natural number is $x=3$.

The greater of the two consecutive natural numbers is:

$x+1=3+1=4$

Verification:

The two consecutive natural numbers are 3 and 4.

Their product is $3\times 4=12$, which matches the given condition.

Hence, the greater of the two numbers is 4.