# 1439 and Level 6

You know the factors of 49, but to complete this puzzle, you will also have to determine the answers to a few questions:

Will the common factor of 24 and 32 be 4 or 8?
Will the common factor of 20 and 40 be 4, 5, or 10?
Will the common factor of 27 and 9 be 3 or 9?

Don’t guess and check! Look at the other clues, and some of the possibilities will be eliminated*. Once you’ve found the next clue to use, continue using logic until the whole puzzle is completed. Print the puzzles or type the solution in this excel file: 10 Factors 1432-1442

• 1439 is a prime number.
• Prime factorization: 1439 is prime.
• 1439 has no exponents greater than 1 in its prime factorization, so √1439 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1439 has exactly 2 factors.
• The factors of 1439 are outlined with their factor pair partners in the graphic below. How do we know that 1439 is a prime number? If 1439 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1439. Since 1439 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1439 is a prime number.

* Did you notice that either one of the 24’s or 6 must use a 3 because only two 6s are allowed to be used as factors? What does that tell you about the common factor of 27 and 9?

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