Today’s Puzzle:
Will Cupid’s Arrow hit you right in your heart this year? Who knows? Solving this puzzle might help! It’s a level 3 puzzle so begin with the clues in the top row, then work your way down the puzzle row by row until you have found all the factors.
Factors of 1775:
- 1775 is a composite number.
- Prime factorization: 1775 = 5 × 5 × 71, which can be written 1775 = 5² × 71.
- 1775 has at least one exponent greater than 1 in its prime factorization so √1775 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1775 = (√25)(√71) = 5√71.
- 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 1775 has exactly 6 factors.
- The factors of 1775 are outlined with their factor pair partners in the graphic below.
More About the Number 1775:
1775 is the difference of two squares in three different ways:
888² – 887² = 1775,
180² – 175² = 1775, and
48² – 23² = 1775.
1775 is the hypotenuse of two Pythagorean triples:
497-1704-1775, calculated from (7-24-25) times 71, and
1065 1420 1775, calculated from (3-4-5) times 355.
From OEIS.org, we learn that 1775 is one of the numbers in this Fibonacci-like series:
1, 7, 8, 15, 23, 38, 61, 99, 160, 259, 419, 678, 1097, 1775, . . .
Did you notice that 1+7=8, 7+8=15, and so forth? That’s why it’s called a Fibonacci-like series.
1775 is the repdigit PP in base 70. P is the 25th number in base 70. Thus,
25(70) + 25(1) = 25(71) = 1775.