Today’s Puzzle:

All of the triangles in the image below are similar. How many similar triangles are there in the image? Why are they similar? Hint: If I were counting them, I would list all the triangles by writing each one indicating the sides in this order every time: the smallest, the medium, and the longest side. Don’t forget to list ΔLKJ. It’s pretty tiny!

Factors of 1779:

• 1779 is a composite number.
• Prime factorization: 1779 = 3 × 593.
• 1779 has no exponents greater than 1 in its prime factorization, so √1779 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 1779 has exactly 4 factors.
• The factors of 1779 are outlined with their factor pair partners in the graphic below.

More About the Number 1779:

1779 is the hypotenuse of a Pythagorean triple:
1104-1395-1779, which is 3 times (368-465-593).

From OEIS.org we learn that 1779 = 10,016,218,555,281, and that’s the smallest 4th power that has 14 digits.

1779 is palindrome 323 in base 24 because
3(24²) + 2(24) + 3(1) = 1779.