Today’s Puzzle:

It’s almost Valentine’s Day! Enjoy this heart-shaped multiplication table puzzle! You only need to know one set of ten math facts to complete this puzzle, but which set is it? The two’s? the three’s? the four’s? or something different? You CAN figure it out, so give it a try! There is only one solution.

Factors of 1773:

Does 1+7+7+3 = a number divisible by 3? I’ve played enough cribbage to know instantly that 1+7+7=15. Add the remaining 3 to the 15, and we get 18, a number divisible by both 3 and 9, so 1773 is divisible by both 3 and 9.

• 1773 is a composite number.
• Prime factorization: 1773 = 3 × 3 × 197, which can be written 1773 = 3² × 197.
• 1773 has at least one exponent greater than 1 in its prime factorization so √1773 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1773 = (√9)(√197) = 3√197.
• The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1773 has exactly 6 factors.
• The factors of 1773 are outlined with their factor pair partners in the graphic below.

More About the Number 1773:

1773 is the sum of two squares:
42² + 3² =1773.

1773 is the hypotenuse of one Pythagorean triple:
252-1755-1773, calculated from 2(42)(3), 42² – 3², 42² + 3².
It is also 9(28-195-197).

1773 is palindrome 909 in base 14 because
9(14²) + 0(14) + 9(1) = 1773.