# 1749 Happy Valentine’s Day!

### Today’s Puzzle:

Here’s one more Valentine’s puzzle for you to do. Enjoy!

### Factors of 1749:

1749 is divisible by 3 because 7 is half of 14 so any 3-digit number made from the digits 714 in any order is divisible by 3, and of course, 9 is divisible by 3.

1749 is divisible by 11 because 1 – 7 + 4 – 9 = -11, a multiple of 11.

• 1749 is a composite number.
• Prime factorization: 1749 = 3 × 11 × 53.
• 1749 has no exponents greater than 1 in its prime factorization, so √1749 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 1749 has exactly 8 factors.
• The factors of 1749 are outlined with their factor pair partners in the graphic below.

### More About the Number 1749:

1749 is the hypotenuse of a Pythagorean triple:
924-1485-1749 which is 33 times (28-45-53).

1749 is the difference of two squares in FOUR different ways:
875² – 874² = 1749,
293² – 290² = 1749,
85² – 74² = 1749, and
43² – 10² = 1749.