### 987 Christmas Star

Today’s puzzle is a lovely Christmas star whose golden beams shine throughout the dark night. Solving this puzzle could also enlighten your mind.

Print the puzzles or type the solution in this excel file: 10-factors-986-992

987 is made from three consecutive numbers so it is divisible by 3.

It is also the sixteen number in the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, **987**, . . .

987 is a palindrome when written in base 11 or base 29:

818 in BASE 11 because 8(121) + 1(11) + 8(1) = 987

151 in BASE 29 because 1(29²) + 5(29) + 1(1) = 987

- 987 is a composite number.
- Prime factorization: 987 = 3 × 7 × 47
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 987 has exactly 8 factors.
- Factors of 987: 1, 3, 7, 21, 47, 141, 329, 987
- Factor pairs: 987 = 1 × 987, 3 × 329, 7 × 141, or 21 × 47
- 987 has no square factors that allow its square root to be simplified. √987 ≈ 31.416556

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