# 1047 and Level 4

There are a couple of clues in this puzzle that might be a little tricky, but I know you won’t let that stop you from finding its solution. Puzzles are fun, so have fun with this one. Print the puzzles or type the solution in this excel file: 12 factors 1044-1053

What do I know about the number 1047?

• 1047 is a composite number.
• Prime factorization: 1047 = 3 × 349
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1047 has exactly 4 factors.
• Factors of 1047: 1, 3, 349, 1047
• Factor pairs: 1047 = 1 × 1047 or 3 × 349
• 1047 has no square factors that allow its square root to be simplified. √1047 ≈ 32.357379 1047 is the hypotenuse of a Pythagorean triple:
540-897-1047 which is 3 times (180-299-349)

It is also a palindrome in a couple of bases:
It’s 343 in BASE 18 because 3(18²) + 4(18) + 3(1) = 1047, and
2H2 in BASE 19 (H is 17 base 10) because 2(19²) + 17(19) + 2(1) = 1047

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