Problem Analysis: We need to find the larger of two consecutive positive natural numbers whose product is 930.
Finding the Consecutive Numbers
Let the two consecutive positive natural numbers be represented by $n$ and $n+1$.
According to the problem statement, their product is 930:
$ n(n+1) = 930 $Expand the equation:
$ n^2 + n = 930 $Rearrange into a standard quadratic equation:
$ n^2 + n - 930 = 0 $Solving the Equation
We can solve this equation by factoring or estimation.
- Estimation Method: Since the numbers are consecutive, they are close to the square root of their product. Calculate the approximate square root of 930: $ \sqrt{930} \approx 30.5 $ This suggests the two consecutive numbers are likely 30 and 31.
- Verification: Check if the product of 30 and 31 is 930: $ 30 \times 31 = 930 $ This confirms that the two consecutive numbers are 30 and 31.
Identifying the Greater Number
The two consecutive positive natural numbers are 30 and 31.
The greater of these two numbers is 31.
Similar Questions
- Find the smallest perfect square number which must be added to the number 12519 to get a perfect square number.
- Find the smallest number which must be subtracted from 63535 to make it a perfect square.
- The sum of first '$n$' natural numbers is:
- $(41^{43} + 43^{43})$ is divisible by:
- Find the difference of the place and face values of 6 in 516372.
- The face value of 8 in 758639 is:
- The product of two consecutive natural numbers is 182. The greater of the two numbers is:
- The value of $1+2+3+...+30+31+30+29+...+3+2+1 =$ ?
- Find the least number which must be added to the number 6412 to get a perfect square.
- Find the sum of the face values of 6 and 5 in 61827354.
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 ?
