The clues in one of the columns for this puzzle as well as one of the rows are 9 and 3. You will need to figure out where to put the factors 1, 3, 3, and 9 to make those clues work. You might think it doesn’t matter where you write those factors, but believe me, it does matter. My advice: Don’t start with those clues. Find another logical place to start. Good luck with this one!

Print the puzzles or type the solution in this excel file: 10-factors-1242-1250

Here are some facts about the number 1250:

- 1250 is a composite number.
- Prime factorization: 1250 = 2 × 5 × 5 × 5 × 5, which can be written 1250 = 2 × 5⁴
- The exponents in the prime factorization are 1 and 5. Adding one to each and multiplying we get (1 + 1)(4 + 1) = 2 × 5 = 10. Therefore 1250 has exactly 10 factors.
- Factors of 1250: 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250
- Factor pairs: 1250 = 1 × 1250, 2 × 625, 5 × 250, 10 × 125, or 25 × 50
- Taking the factor pair with the largest square number factor, we get √1250 = (√625)(√2) = 25√2 ≈
**35**.**3553**4

1250 is the sum of consecutive squares two different ways:

193 + 197 + 199 + 211 + 223 + 227 = 1250

619 + 631 = 1250

1250 is the sum of two squares THREE different ways:

31² + 17² = 1250

25² + 25² = 1250

35² + 5² = 1250

1250 is the hypotenuse of FOUR Pythagorean triples:

750-1000-1250 which is (3-4-**5**) times **250**,

672-1054-1250 which is **2** times (336-527-**625**) and

can also be calculated from 31² – 17², 2(31)(17), 31² + 17²,

440-1170-1250 which is **10** times (44-117-**125**), and

350-1200-1250 which is (7-24-**25**) times **50** and

can also be calculated from 2(35)(5), 35² – 5², 35² + 5²