### Today’s Puzzle:

I like multiples of 111, including 1554. What cool patterns do you notice if a 2-digit number is multiplied by 111 as shown in the graphic below:

### A Factor Tree for 1554:

Here’s a factor tree for 1554 that begins with the factor pair 14 × 111:

### Factors of 1554:

- 1554 is a composite number.
- Prime factorization: 1554 = 2 × 3 × 7 × 37
- 1554 has no exponents greater than 1 in its prime factorization, so √1554 cannot be simplified.
- The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1554 has exactly 16 factors.
- The factors of 1554 are outlined with their factor pair partners in the graphic below.

### More about the Number 1554:

1554 is the hypotenuse of a Pythagorean triple:

504-1470-1554, which is (12-35-**37**) times **42**.