A Multiplication Based Logic Puzzle

741 and Level 3

Look at 741’s three digits: 4 = (1/2)(7 + 1) so 741 is divisible by 3.

  • 741 is a composite number.
  • Prime factorization: 741 = 3 x 13 x 19
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 741 has exactly 8 factors.
  • Factors of 741: 1, 3, 13, 19, 39, 57, 247, 741
  • Factor pairs: 741 = 1 x 741, 3 x 247, 13 x 57, or 19 x 39
  • 741 has no square factors that allow its square root to be simplified. √741 ≈ 27.221315.

741-factor-pairs

Here is today’s puzzle:

741 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2016-01-11

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Here are more 741 number facts:

19 x 39 = 741. Since 19 and 39 are both exactly 10 away from their average, 29, we know that 741 is exactly 100 away from 29² = 841.

19 x 39 = (38/2 )(38 + 1) so 741 is the 38th triangular number.

741 can be expressed as the sum of consecutive numbers seven ways:

  • 370 + 371 = 741; that’s 2 consecutive numbers.
  • 246 + 247 + 248 = 741; that’s 3 consecutive numbers.
  • 121 + 122 + 123 + 124 + 125 + 126 = 741; that’s 6 consecutive numbers.
  • 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 = 741; that’s 13 consecutive numbers.
  • 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 = 741; that’s 19 consecutive numbers.
  • 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 = 741; that’s 26 consecutive numbers.
  • 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 = 741; that’s 38 consecutive numbers confirming that 741 is the 38th triangular number.

Since 13 is one of its factors, 741 is the hypotenuse of the Pythagorean triple 285-684-741. The greatest common factor of those 3 numbers can be found in the same factor pair as 13.

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A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. (None of the factors are greater than 12.)  Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

741 Factors

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