### Today’s Puzzle:

If you were a child in Hungary, you might have found some *virgács* and some candy in your boot this morning. *Mikulás* (St. Nick) would have given you the candy because of how good you’ve been this year, and the *virgács* for those times you weren’t so good.

This *virgács *and candy puzzle is like a mixed-up multiplication table. It is a lot easier to solve because I made it a level 3 puzzle. First, find the common factor of 56 and 72 that will allow only numbers between 1 and 12 to go in the first column. Put the factors in the appropriate cells, then work your way down the puzzle, row by row until each number from 1 to 12 is in both the first column and the top row.

### Factors of 1698:

- 1698 is a composite number.
- Prime factorization: 1698 = 2 × 3 × 283.
- 1698 has no exponents greater than 1 in its prime factorization, so √1698 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 1698 has exactly 8 factors.
- The factors of 1698 are outlined with their factor pair partners in the graphic below.

### More About the Number 1698:

1698 = 2(849)(1), so it is a leg in the Pythagorean triple calculated from

2(849)(1), 849² – 1², 849² + 1².

1698 = 2(283)(3), so it is a leg in the Pythagorean triple calculated from

2(283)(3), 283² – 3², 283² + 3².