Finding Consecutive Natural Numbers with a Given Product
Let the two consecutive natural numbers be represented by $n$ and $n+1$. The problem states that their product is 182.
Formulating the Equation
We can write the relationship as an equation:
$ n(n+1) = 182 $Solving for the Numbers
Expand the equation:
$ n^2 + n = 182 $Rearrange it into a standard quadratic equation:
$ n^2 + n - 182 = 0 $We can solve this quadratic equation by factoring. We need two numbers that multiply to -182 and add to 1. These numbers are 14 and -13.
Factor the quadratic equation:
$ (n + 14)(n - 13) = 0 $This gives two possible values for $n$:
- $n + 14 = 0 \implies n = -14$
- $n - 13 = 0 \implies n = 13$
Since we are looking for natural numbers (positive integers), we choose $n = 13$.
Identifying the Greater Number
The two consecutive natural numbers are $n = 13$ and $n+1 = 14$.
We can verify their product: $13 \times 14 = 182$.
The question asks for the greater of the two numbers.
The greater number is $14$.
This matches Option A.
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Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
