# 168 and the Very Inspiring Blogger Award

### 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:

2. Blogbloggerbloggest
4. established1962
5. Hummingtop
6. colleenyoung.wordpress.com
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.