Month: December 2015

698 The week a single post went viral in two countries

/ ivasallay / 4 Comments

Since this site is called Find the Factors and each post is numbered, I factor those numbers and write some interesting facts about them.

For example, this is my 698th post, so I’ll give its factoring information here:

  • 698 is a composite number.
  • Prime factorization: 698 = 2 x 349
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 698 has exactly 4 factors.
  • Factors of 698: 1, 2, 349, 698
  • Factor pairs: 698 = 1 x 698 or 2 x 349
  • 698 has no square factors that allow its square root to be simplified. √698 ≈ 26.4196896. (Close to the beginning of the square root we see 698 backwards as well as the magic number 689.)

Now I’ll share some other interesting information about the number 698:

698 is the hypotenuse of Pythagorean triple 360-598-698.

OEIS.org informs us that 3^2 + 4^3 + 5^4 = 698.

173 + 174 + 175 + 176 = 698 so it is the sum of four consecutive numbers.

698 is a palindrome in two different bases:

  • 22322 BASE 4; note 2(256) + 2(64) + 3(16) + 2(4) + 2(1) = 698
  • 585 BASE 11; note 5(121) + 8(11) + 5(1) = 698

And 698 is a permutation of 689, the number of my most viewed post of all time. I wrote that post a week ago on Tuesday, and all it contained was some interesting information about the number 689. There was nothing earth shattering in it.

However, Wednesday evening, Denise Gaskins shared that 689th post on her facebook page, Let’s Play Math. (She has so many good things on her facebook page.)

689 Let's Play Math

The 17 shares you see on this facebook post is NOT the whole picture; it is only the beginning.

Other than my homepage/archives, my most viewed post has now become “What Makes 689 Amazing” It has also been shared on facebook over 2000 times!

Top Posts all time

Here is the breakdown of the number of views it received each day:

Number of Views Per Day

Usually most of my views come from the United States and the United Kingdom, but there was a definite although temporary shift last week. Here are the four top counties viewing this blog from last Thursday to Sunday:

Blog Views

I was quite puzzled by why this blog post went viral in Hong Kong and Taiwan. Perhaps Alan Parr’s (wbhs1962) comment about a funny experience with the number 689 broke the ice. Eventually a few readers from Hong Kong and Taiwan enlightened me about the viral interest in this particular number. Those comments were all quite fascinating and an educational experience for me. I invite you to read them as well.

697 and Level 3

/ ivasallay / Leave a comment
  • 697 is a composite number.
  • Prime factorization: 697 = 17 x 41
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 697 has exactly 4 factors.
  • Factors of 697: 1, 17, 41, 697
  • Factor pairs: 697 = 1 x 697 or 17 x 41
  • 697 has no square factors that allow its square root to be simplified. √697 ≈ 26.40075756.

Here is today’s factoring puzzle:

 

697 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-11-30

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Here are some more thoughts about the number 697:

Because both of its factors are hypotenuses of Pythagorean triples, 697 is the hypotenuse of FOUR Pythagorean triples:

  • 153-680-697
  • 185-672-697
  • 328-615-697
  • 455-528-697

Two of those triples are primitive, and two are not. Can you find the greatest common factor for each one that is not primitive?

697 is palindrome 151 in BASE 24; note that 24² = 576, and 1(576) + 5(24) + 1(1) = 697.

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A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. (None of the factors are greater than 12.)  Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

697 Factors

696 There are lots of goodies in this Christmas Stocking

/ ivasallay / Leave a comment
  • 696 is a composite number.
  • Prime factorization: 696 = 2 x 2 x 2 x 3 x 29, which can be written 696 = (2^3) x 3 x 29
  • The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16. Therefore 696 has exactly 16 factors.
  • Factors of 696: 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696
  • Factor pairs: 696 = 1 x 696, 2 x 348, 3 x 232, 4 x 174, 6 x 116, 8 x 87, 12 x 58, or 24 x 29
  • Taking the factor pair with the largest square number factor, we get √696 = (√4)(√174) = 2√174 ≈ 26.38181.

Today’s puzzle is meant to look like a Christmas stocking or boot that can be filled with lots of little treasures.

696 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-11-30

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What other facts did I find about the number 696?

696 is the sum of all the prime numbers from 71 to 103. Do you know what those eight prime numbers are?

696 is also the sum of consecutive odd numbers 347 and 349 which just happen to also be consecutive prime numbers.

Because 696 is a multiple of 29, it is the hypotenuse of Pythagorean triple 480-504-696. What is the greatest common factor of those three numbers?

696 is a palindrome in two different bases

  • 696 BASE 10; note that 6(100) + 9(10) + 6(1) = 696
  • OO BASE 28; note that O BASE 28 is equivalent to 24 in BASE 10, and  24(28) + 24(1) = 696

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696 Factors