Properties of 2024

The number 2024, at a glance, may just look-like another number. However, viewing closely shows that it has many unique mathematical properties that will never be seen again in any other year. These properties distinguish it from other years, which make it special. These traits are definitely something to think about during the year 2024!

The number 2024 is an even, 4 digit, composite number with a prime factorization of 23*11*23, making it have 16 divisors summing to 4320. The sum of its prime factors is 40 when allowing for repeats and 36 when counting distinctly. Its divisors include: 1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, and 2024. The prime number that is closest to it is 2027 and the prime before it is 2017 (Properties of number 2024).

(What is a prime number?)

2024 in binary is 11111101000 (base 2). 2024 in octal is equal to 37508 in base 8. In duodecimal and hexadecimal, it’s the same as 1208 (base 12) and 7*108 (base 16) respectively.

2024 = 3*104 + 7*103 + 5*102 + 0*101

2024 = 1*124 + 2*123 + 0*122 + 8*121

2024 = 7*169 + 0(168 +...+ 161)

The number 2024 can be represented by the difference of two squares 45^2 - 1^2, factoring to (45+1)(45-1) or 46*44. This is a special property because the next year that will be a difference of two squares is 2035, 11 years from now, which would be written as 46^2 -9^2, (46+9)(46-9), or 55*37. 2024 is also the sum of cubes from 2 through 9 and from -1 through 9.

Additionally, it is a tetrahedral number since it is the sum of the first 22 triangular numbers, starting from 1, 3, 6, 10, 15, 21, 28, 36, 45, etc. Some examples of triangular numbers with a visualization are below (Properties of the number 2024):

(Maths in a minute: Triangular numbers)

Suppose function f(x) = x^2+ 2x, which would make f(44) = 2024. If 44 was split into 20 + 24, the function f(x) could be written as (20+24) + (20+24)(20+24) + (20+24) or (20+24)2 + 2(20+24), which is symmetrical.

2024 is equivalent to 24 choose 3, which can be written as (24!)/(3!(24-3)!) and makes it a binomial coefficient. Definition below:

It can further be written as the sum of consecutive natural numbers, 2024 = 77 +..+ 2099, and is equal to 2^10 + 10^3 as well as (3!⋅2!+2!)3 − 3!

2024 written as the sum of fibonacci numbers:

1597+377+34+13+31597+377+34+13+2+11597+377+34+8+5+31597+233+144+34+13+3987+610+377+34+13+31597+377+34+8+5+2+11597+377+21+13+8+5+31597+233+144+34+13+2+11597+233+144+34+8+5+31597+233+89+55+34+13+3987+610+377+34+13+2+1987+610+377+34+8+5+3987+610+233+144+34+13+31597+377+21+13+8+5+2+11597+233+144+34+8+5+2+11597+233+144+21+13+8+5+31597+233+89+55+34+13+2+11597+233+89+55+34+8+5+3987+610+377+34+8+5+2+1987+610+377+21+13+8+5+3987+610+233+144+34+13+2+1987+610+233+144+34+8+5+3987+610+233+89+55+34+13+31597+233+144+21+13+8+5+2+11597+233+89+55+34+8+5+2+11597+233+89+55+21+13+8+5+3987+610+377+21+13+8+5+2+1987+610+233+144+34+8+5+2+1987+610+233+144+21+13+8+5+3987+610+233+89+55+34+13+2+1987+610+233+89+55+34+8+5+31597+233+89+55+21+13+8+5+2+1987+610+233+144+21+13+8+5+2+1987+610+233+89+55+34+8+5+2+1987+610+233+89+55+21+13+8+5+3987+610+233+89+55+21+13+8+5+2+1 (OpenAI)

These are just some of the many properties of the number 2024. Try operating on the number and see if you can find any properties not mentioned here.

References:

Properties of number 2024. (n.d.). https://www.numbersaplenty.com/2024

Properties of the number 2024. (n.d.). https://www.numberempire.com/2024

OpenAI. (2024). ChatGPT (April 2023 version) [Large language model]. https://chat.openai.com

Maths in a minute: Triangular numbers. Plus Maths. (2020, November 24). https://plus.maths.org/content/maths-minute-triangular-numbers

What is a prime number?. Wonderopolis. (n.d.). https://wonderopolis.org/wonder/what-is-a-prime-number