I Was Nominated for the Very Inspiring Blogger Award!

Nerdinthebrain is a very well-rounded and inspiring blogger. I feel quite honored that she nominated me for the Very Inspiring Blogger Award.

Just two little rules for accepting this award:

1) The nominee shall display the Very Inspiring Blogger Award logo on her/his blog, and link to the blog they got nominated from.

2) The nominee shall nominate fifteen (15) bloggers she/he admires, by linking to their blogs and informing them about it.

Because this award has these requirements, it may seem like a modern version of a chain letter, but it also appears to be a great way to step out of our comfort zones. It helps us read posts and share ideas with people with whom we have a little something in common but just don’t know it yet. Here are my 15 nominees:

1. Beyondtraditionalmath
2. Blogbloggerbloggest
3. Crazygoodreaders DYSLEXIA DIGEST
4. established1962
5. Hummingtop
6. colleenyoung.wordpress.com
7. MY MATH-Y ADVENTURES
8. Nebusresearch (He actually has 2 great blogs.)
9. NumberLovingBeagle
10. PeopleStoryNetwork
11. Bookzoompa
12. RobertLovesPi
13. http://mathtuition88.com/
14. VisuallyLiteral (Nancy Tordai Photography)
15. MarekBennett

Congratulations to each of you. (I’ll do the informing tomorrow because I’ve already spent more time than usual on the internet today.)

Factors of 168:

√168 ≈ 12.96148. Let’s divide 168 by each number from 1 to 12 to find its factor pairs.

The prime factorization of 168 is 2³ × 3 × 7.
Adding 1 to each of the exponents in the prime factorization and multiplying, we get
(3 + 1)(1 + 1)(1 + 1) = 4 × 2 × 2 = 12. Notice that 168 has exactly 12 factors.

More About the Number 168:

Four of those factor pairs are made up of only even numbers, so 168 is the difference of two squares four different ways:
43² – 41² = 168,
23² – 19² = 168,
17² – 11² = 168,
13² – 1² = 168.

Since 168 is 3 × 56, it is the sum of three consecutive numbers with 56 as the middle number:
55 + 56 + 57 = 168.

Since 168 is 7 × 24, it is the sum of seven consecutive numbers with 24 as the middle number:
21 + 22 + 23 + 24 + 25 + 26 + 27 = 168.

Finally, since 168 is divisible by 8, but not by 16, it is the sum of 16 consecutive numbers:
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 168.

As a consequence of that last mathematical fact, here’s another way to make 168:
18² – 17² + 16² – 15² + 14² – 13² + 12² – 11² + 10² – 9² + 8² – 7² + 6² – 5² + 4² – 3² = 168.
I bet you weren’t expecting that!

168 = 6 × 28, so 168 is the product of the first two perfect numbers! Why are those numbers perfect? Each of them is the sum of their divisors:
6 = 1 + 2 + 3, and
28 = 1 + 2 + 4 + 7 + 14.

168 is a repdigit in several other bases:
It’s CC in base 13 because 12(13+1) = 168,
88 in base 20 because 8(20+1) = 168,
77 in base 23 because 7(23+1) = 168,
66 in base 27 because 6(27+1) = 168,
44 in base 41 because 4(41+1) = 168,
33 in base 55 because 3(55+1) = 168,
22 in base 83 because 2(83+1) = 168, and
11 in base 167 because 1(167+1) = 168.