A Multiplication Based Logic Puzzle

We can find some of the factors of 402 rather quickly. It’s even, so 2 is a factor. 4 + 0 + 2 = 6, a multiple of 3, so 3 is also a factor. Six, then, would also be a factor. How many factors does 402 have and what are they? Scroll down to the end of the post to find out!

Nerd in the Brain created the-Spectacular-Blog-Award. This is how she describes it: “🙂It’s a simple award with no strings attached…no questions to answer, no specific number of people to nominate, no obligation. Recipients can just bask in the glory of knowing that another blogger thinks they’re super-awesome.” 🙂 

She continued, “This award is not just for me to give to people! If you want to let another blogger know that you think they’re fantastic, you go right ahead and snag this little award and pass it along to them. Share, share!” Keep Nerd in the Brain in the loop if you give someone this award.

So I for one am “snagging” this award to pass on to someone else:

Update: I gave the award to Abyssbrain whose blog, Mathemagicalsite.wordpress.com, has, unfortunately, been deleted.

The only thing I can think of to quell my disappointment is to find a couple more things about the number 402 and add them to this post:

Here are five ways 402 is the sum of three squares:

  • 20² + 1² + 1² = 402
  • 19² + 5² + 4² = 402
  • 17² + 8² + 7² = 402
  • 16² + 11² + 5² = 402
  • 13² + 13² + 8² = 402

402 is 123 in BASE 19 because 1(19²) + 2(19¹) + 3(19°) = 402.

  • 402 is a composite number.
  • Prime factorization: 402 = 2 x 3 x 67
  • 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 x 2 x 2 = 8. Therefore 402 has exactly 8 factors.
  • Factors of 402: 1, 2, 3, 6, 67, 134, 201, 402
  • Factor pairs: 402 = 1 x 402, 2 x 201, 3 x 134, or 6 x 67
  • 402 has no square factors that allow its square root to be simplified. √402 ≈ 20.0499

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Comments on: "402 and Passing Along The Spectacular Blog Award" (4)

  1. Oh, math and passing on the Spectacular Blog Award?!? You’ve made my day much better! 😀

    Liked by 1 person

  2. abyssbrain said:

    Thank you for appreciating my blog. Your blog is spectacular too!

    Liked by 1 person

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