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.
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Important Questions from Number System
What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?
Which sequence is correct to represent the hierarchical chain of number system?
(Where N - Natural Numbers
W - Whole Numbers
Q - Rational Numbers
Z - Integers)
What must be added to 45680 to make it exactly divisible by 9?
How many zeroes are there at the end of the following product?
1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60
Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
