# 1507 and Level 6

### Today’s Puzzle:

Level six puzzles are designed to be tricky, but if you examine the clues, there is a logical place to begin, and logic can help you complete the entire puzzle. ### Factors of 1507:

• 1507 is a composite number.
• Prime factorization: 1507 = 11 × 137.
• 1507 has no exponents greater than 1 in its prime factorization, so √1507 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 1507 has exactly 4 factors.
• The factors of 1507 are outlined with their factor pair partners in the graphic below. ### More about the Number 1507:

1507 is the hypotenuse of a Pythagorean triple.
968-1155-1507

A divisibility trick tells us that all of the numbers in that triple are divisible by 11:
9 – 6 + 8 = 11,
1 – 1 + 5 – 5 = 0,
1 – 5 + 0 – 7 = -11.

Yes, you would need to understand negative numbers for that last one, but 11, 0, and -11 can all be evenly divided by 11 so the corresponding numbers are also divisible by 11.

In fact, 968-1155-1507 is just 11 times (88-105-137).