1378 and Level 3

The first row with a clue has a 14 in it. Use that 14 and the clue in the same column, to figure out where to put one of the factor pairs of 14 in this puzzle.  Only use factor pairs where both numbers are from 1 to 10. Then work your way down the puzzle, row by row until you have found all the factors of this level 3 puzzle. The completed puzzle will look like a multiplication table with the factors in a different order.

Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here is some information about the puzzle number, 1378:

• 1378 is a composite number.
• Prime factorization: 1378 = 2 × 13 × 53
• 1378 has no exponents greater than 1 in its prime factorization, so √1378 cannot be simplified.
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1378 has exactly 8 factors.
• The factors of 1378 are outlined with their factor pair partners in the graphic below.

1378 is the 52nd triangular number because (52)(53)/2 = 1378.

1378 is the hypotenuse of FOUR Pythagorean triples:
222-1360-1378 which is 2 times (111-680-689)
530-1272-1378 which is (5-12-13) times 106
728-1170-1378 which is 26 times (28-45-53)
800-1122-1378 which is 2 times (400-561-689)

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