### Today’s Puzzle:

1547 is the 13th hexagonal pyramidal number. Looking at the graphic that I made below of 1547 tiny squares, can you determine what the prime factorization of 1547 is?

### Factors of 1547:

- 1547 is a composite number.
- Prime factorization: 1547 = 7 × 13 × 17.
- 1547 has no exponents greater than 1 in its prime factorization, so √1547 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 1547 has exactly 8 factors.
- The factors of 1547 are outlined with their factor pair partners in the graphic below.

### More about the Number 1547:

1547 is the hypotenuse of FOUR Pythagorean triples:

147-1540-1547, which is **7** times (21-220-**221**),

595-1428-1547, which is (5-12-**13**) times **119**,

728-1365-1547, which is (8-15-**17**) times **91**, and

980-1197-1547, which is **7** times (140-171-**221**).