A student opens a mathematics book to two facing pages. The product of the page numbers is 2352. Find the page numbers.
The square root of 2352 = 48.497422
That gives you a big clue.
So the first page is 48 and the second page is 49.
Right!
48,49
To find the page numbers, we need to determine two consecutive integers whose product is 2352.
One way to solve this is to start by finding the prime factorization of 2352:
2352 = 2 * 2 * 2 * 3 * 7 * 7
From the prime factorization, we can see that 2352 can be expressed as the product of two integers in several ways. However, since we are looking for two consecutive page numbers, we can focus on pairs of factors that differ by 1.
Starting with the largest prime factor, 7, we can test different pairs of factors until we find a pair that differs by 1:
7 * 336 = 2352
Let's check if 336 and 337 are the two consecutive page numbers:
336 * 337 = 113,232
Since the product is not equal to 2352, we need to continue searching.
Next, we move on to the next largest prime factor, 3:
3 * 784 = 2352
Is 783 one less than 784?
783 + 1 = 784
Now, we have found the two consecutive page numbers:
The first page number is 783, and the second page number is 784.
Therefore, the page numbers are 783 and 784.