Understanding the Problem

The question asks us to find the larger of two consecutive natural numbers whose product equals 6.

• Natural numbers are positive whole numbers starting from 1 (1, 2, 3, ...).
• Consecutive natural numbers are numbers that follow each other directly, like 1 and 2, or 5 and 6.
• The product means the result of multiplying the two numbers together.

Algebraic Approach to Find Consecutive Numbers

Let's represent the two consecutive natural numbers using algebra. If we call the smaller number '$n$', then the next consecutive number will be '$n+1$' (since they are natural numbers).

We are given that their product is 6. So, we can write the equation:

$n \times (n+1) = 6$

Solving the Equation

1. Expand the equation: Multiply '$n$' by both terms inside the parentheses. $n^2 + n = 6$
2. Rearrange into a quadratic equation: Move all terms to one side to set the equation to zero. $n^2 + n - 6 = 0$
3. Factor the quadratic equation: We need to find two numbers that multiply to -6 and add up to +1 (the coefficient of the '$n$' term). These numbers are +3 and -2. $(n+3)(n-2) = 0$
4. Solve for '$n$': Set each factor equal to zero and solve.
   • $n + 3 = 0 \implies n = -3$
   • $n - 2 = 0 \implies n = 2$

Choosing the Correct Value for '$n$'

The question specifies that the numbers must be natural numbers. Natural numbers are positive integers (1, 2, 3,...).

• The value $n = -3$ is negative, so it's not a natural number. We discard this solution.
• The value $n = 2$ is a positive integer, so it is a natural number. This is our valid value for the smaller number.

Identifying the Numbers and the Greater Number

We found that the smaller number, '$n$', is 2.

• The smaller number is $n = 2$.
• The greater consecutive number is $n+1 = 2 + 1 = 3$.

The two consecutive natural numbers are 2 and 3.

Verification

Let's check if their product is indeed 6:

$2 \times 3 = 6$

The condition is satisfied.

Determining the Greater Number

The two numbers are 2 and 3. Comparing them, the greater number is 3.

Alternative Method: Testing Options

You can also solve this problem by testing the given options:

By testing the options, we see that when the greater number is 3, the smaller consecutive number is 2, and their product is 6. Therefore, 3 is the correct answer.

Conclusion

The two consecutive natural numbers are 2 and 3. The greater of these two numbers is 3.