### Today’s Puzzle:

Where do the Factors 1-12 belong on this multiplication table puzzle?

### Factors of 1469:

- 1469 is a composite number.
- Prime factorization: 1469 = 13 × 113
- 1469 has no exponents greater than 1 in its prime factorization, so √1469 cannot be simplified.
- The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1469 has exactly 4 factors.
- The factors of 1469 are outlined with their factor pair partners in the graphic below.

### Other Facts about the Number 1469:

1469 is the sum of two squares in two different ways:

38² + 5² = 1469

37² + 10² = 1469

1469 is the hypotenuse of FOUR Pythagorean triples:

195-1456-1469 which is **13** times (15-112-**113**)

380-1419-1469 calculated from 2(38)(5), 38² – 5², 38² + 5²

565-1356-1469 which is (5-12-**13**) times **113**

740-1269-1469 calculated from 2(37)(10), 37² – 10², 37² + 10²