# 1527 Not a Haunted House

### Today’s Puzzle:

We see plenty of pumpkins on doorsteps this time of year, so I put a few in this puzzle. The puzzle looks a bit like a house, but certainly not a haunted house. Can you write the numbers from 1 to 10 in both the first column and the top row so that the given number clues are the products of those numbers?

Here’s the same puzzle without the added colorful embellishments: ### Factors of 1527:

• 1527 is a composite number.
• Prime factorization: 1527 = 3 × 509.
• 1527 has no exponents greater than 1 in its prime factorization, so √1527 cannot be simplified.
• The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1527 has exactly 4 factors.
• The factors of 1527 are outlined with their factor pair partners in the graphic below. ### Another Fact about the Number 1527:

1527 is the hypotenuse of a Pythagorean triple:
660-1377-1527, which is 3 times (220-459-509).