Clues and Strategies:

• Start with large prime numbers. Especially in those 20x20 or 25x25 puzzles, there will be some big numbers, which make it hard to begin. Remember prime numbers has only one possible factorization? Use this property!
• Start with numbers with fewer possible factorization. 15 is a great example; it's either 1-by-15 or 3-by-5. If the first case won't work, then immediately you can conclude that it has to be the second one. BUT, you don't want to try numbers like 36 (5 possibilities) or 60 (6 possibilities) too early. Any misstep may lead you into troubles.
• Numbers with large prime factors can be very helpful. You may encounter 138, for instance. That's a huge number, but notice it has a prime factor 23? (138 = 2 x 3 x 23) That means it must be a long rectangle with a side length of at least 23. Knowing this, you can check how it would fit into your situation. Furthermore, a big area like that often narrows down many possible sizes of other rectangles.

Be familiar with the factorizations. Here's a table of numbers that may not be obvious to you:

Prime Number	Multiples
13	52, 65, 78, 91, 104, 117, 143, 156, 169, 182, 195
17	68, 85, 102, 119, 136, 153, 187
19	76, 95, 114, 133, 152, 171
23	92, 115, 138, 161, 184
29	116, 145, 174
31	124, 155, 186
37	111, 148, 185

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