The common factors of 20 and 40 are 1, 2, **4**, **5**, and **10**. Only the ones in blue will put numbers from 1 to 12 in the top row, as required. Since there is more than one possible common factor, don’t start with those two clues. This is a level 5 puzzle so at least one pair of clues will work to get you started.

Print the puzzles or type the solution in this excel file: 12 factors 1063-1072

Here are a few facts about the number 1067:

- 1067 is a composite number.
- Prime factorization: 1067 = 11 × 97
- 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 1067 has exactly 4 factors.
- Factors of 1067: 1, 11, 97, 1067
- Factor pairs: 1067 = 1 × 1067 or 11 × 97
- 1067 has no square factors that allow its square root to be simplified. √1067 ≈ 32.66497

1067 is the hypotenuse of a Pythagorean triple:

715-792-1067 which is **11** times (65-72-**97**)

We can use the 11 divisibility trick on all the numbers in that triple:

7 – 1 + 5 = **11**

7 – 9 + 2 = **0**

1 – 0 + 6 – 7 =** 0**

to see that all of them can indeed be evenly divided by 11.

1067 is palindrome 1F1 in BASE 26 (F is 15 base 10) because 26² + 15(26) + 1 = 1067

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