### Today’s Puzzle:

Here’s a heart-shaped level 2 puzzle for you to do. Just place all the numbers from 1 to 10 in both the first column and the top row so that those numbers are the factors of the given clues.

Here’s the same puzzle in black and white:

### Factors of 1740:

- 1740 is a composite number.
- Prime factorization: 1740 = 2 × 2 × 3 × 5 × 29, which can be written 1740 = 2² × 3 × 5 × 29.
- 1740 has at least one exponent greater than 1 in its prime factorization so √1740 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1740 = (√4)(√435) = 2√435.
- The exponents in the prime factorization are 2, 1, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 × 2 = 24. Therefore 1740 has exactly 24 factors.
- The factors of 1740 are outlined with their factor pair partners in the graphic below.

### More About the Number 1740:

1740 is the hypotenuse of FOUR Pythagorean triples:

204-1728-1740, which is 3 times (68-576-580),

288-1716-1740, which is 3 times (96-572-580),

1044-1392-1740, which is (3-4-**5**) times **348**, and

1200-1260-1740, which is (20-21-**29**) times **60**.

1740 is palindrome 606 in base 17 because

6(17²) + 0(17) + 6(1) = 1740.

1740 is the difference of two squares in four different ways:

436² – 434² = 1740,

148² – 142² = 1740,

92² – 82² = 1740, and

44² – 14² = 1740.