# 1030 Cupid’s Arrow

Love can often be like a puzzle. When cupid’s arrow hits its mark, at first everything might seem to fall into place, but before long, love starts getting complicated and has to be figured out.

That’s the way this Cupid’s Arrow puzzle is, too. It’s easy to find the logic to start it, but then the logic will be more difficult to see. May you be able to figure out this puzzle as well as the important relationships in your life!

Print the puzzles or type the solution in this excel file: 12 factors 1028-1034

What can I tell you about the number 1030?

It’s the sum of two consecutive prime numbers:
509 + 521 = 1030

It’s the hypotenuse of a Pythagorean triple:
618-824-1030 which is (3-4-5) times 206

It’s palindrome 1102011 in BASE 3 because 3⁶ + 3⁵ + 2(3³) + 3¹ + 3⁰ = 1030

• 1030 is a composite number.
• Prime factorization: 1030 = 2 × 5 × 103
• 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 1030 has exactly 8 factors.
• Factors of 1030: 1, 2, 5, 10, 103, 206, 515, 1030
• Factor pairs: 1030 = 1 × 1030, 2 × 515, 5 × 206, or 10 × 103
• 1030 has no square factors that allow its square root to be simplified. √1030 ≈ 32.09361

# 57 and Cupid’s arrow is on its way!

57 is a composite number. 57 = 1 x 57 or 3 x 19. Factors of 57: 1, 3, 19, 57. Prime factorization: 57 = 3 x 19.

57 is never a clue in the FIND THE FACTORS puzzles.

How do you feel about factoring?

If you will let Cupid hit you with this arrow, you might just fall in love with factors.

Factoring is very important in many levels of mathematics, so enjoying it can be a very good thing.

I love factoring. I hope you will let Cupid’s arrow hit you so you will love factoring, too.

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles.

The factors for last week’s level 3 Puzzle:

Here’s how last week’s puzzle was solved: