### 907 and Level 3

88 is 8 × 11, and 24 is 2 × 12, 3 × 8, or 4 × 6. Those are all their factor pairs in which both factors are less than or equal to 12. There is only one number that is a common factor for both 88 and 24. Write that number in the top cell of the first column and the rest of 88’s factor pair directly above 88 and the rest of 24’s factor pair directly above 24 in the top row.

Next think of a factor pair for 80 in which both factors are less than or equal to 12. You probably thought of 8 × 10, the only factor pair that qualifies. The first column already has an 8, so this 8 must go in the top row above 80. Write 10 in the first column.

The next row doesn’t have a clue, but you already have enough information to write what number must go in the first column. (Hint: it is a number that is already in the top row and can’t go in any other cell in the first column.) If you cannot figure out what goes in this cell, skip that row until later, and figure out what goes in the next cells continuing from the top cell of the first column to the bottom cell. You will fill out the top row at the same time, but each factor 1- 12 will be written above its appropriate clue instead of in order from left to right. Good luck!

Print the puzzles or type the solution on this excel file: 12 factors 905-913

907 is the first prime number since 887. We will not have to wait nearly as long for the next prime number. It will be 911.

907 is palindrome 32023 in BASE 4 because 3(4⁴) + 2(4³) + 0(4²) + 2(4¹) + 3(4º) = 907.

- 907 is a prime number.
- Prime factorization: 907 is prime.
- The exponent of prime number 907 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 907 has exactly 2 factors.
- Factors of 907: 1, 907
- Factor pairs: 907 = 1 × 907
- 907 has no square factors that allow its square root to be simplified. √907 ≈ 30.11644

**How do we know that ****907**** is a prime number?** If 907 were not a prime number, then it would be divisible by at least one prime number less than or equal to √907 ≈ 30.1. Since 907 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, or 29, we know that 907 is a prime number.

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