Number of Rectangles with area 1470?

First we must prime-factorize 1,470 (remember, we are looking for integers that multiply out to 1,470). We see that $1,470=2 \times 3 \times 5\times 7^{2}$ . Adding one to all of the powers (refer to this ), and multiplying together gets 24. So 1,470 has 24 integral factors, but that's not how many sets of 2 numbers that multiply to 1,470 there are. So we divide by 2 to find that there are 12 pairs of numbers that multiply to get 1,470.