2022 Facts and Factors

Today’s Puzzle:

Solve these two multiplication problems and see how mirror-like they are!

Only 50 numbers less than 10000 can make a similar claim to fame:

Countdown to 2022:

Early in 2021, I found a countdown equation for 2022 that also involves its factors. A couple of weeks ago, I found another one. I can’t decide which one I like the best. Even though you can only focus on one equation at a time, the countdown will show both of them concurrently:

2022 Countdown Equations

make science GIFs like this at MakeaGif
Here is a still of the last frame:

 

Factors of 2022:

You might be asked to find the factors of 2022 several times in the coming year.
It’s an even number, so it’s divisible by 2.
It’s also easy to remember that it is divisible by 3 because 2 + 2 + 2 = 6, a multiple of 3.
This graphic may help you remember that it is divisible by 337:
  • 2022 is a composite number.
  • Prime factorization: 2022 = 2 × 3 × 337.
  • 2022 has no exponents greater than 1 in its prime factorization, so √2022 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 2022 has exactly 8 factors.
  • The factors of 2022 are outlined with their factor pair partners in the graphic below.

More About the Number 2022:

2022 is in the hypotenuse of a Pythagorean triple:
1050-1728-2022, which is 6 times (175-288-337).

It is also the short leg in three other Pythagorean triples:
2022-2696-3370, which is (3-4-5) times 674,
2022-340704-340710, which is 6 times (337-56784-56785), and
2022-1022120-1022122, which is 2 times (1011-511060-511061)

2022 uses only 2’s and 0’s in base 10 and in base 3:
2022₁₀ = 2202220₃.

2022 is the sum of positive consecutive numbers in three different ways:

2022 Magic Squares:

All of the above are the facts that I came up with. Lots of people on Twitter have found other facts about 2022. Be sure to check them out!

Tweets Celebrating 2022’s Mathematical Properties:

Here are some tweets about 2022 that I’ve seen on Twitter. I’ll add more as I see them. They are not listed in order of difficulty, but more or less, in the order that I saw them.

 


I’ll end with this thread that you’ll just have to click on to appreciate. It’s packed with tons of mathematical reasons 2022 will a fabulous year!