Numbers·2048
2048
MMXLVIII
100000000000

The number 2048 — factors and divisors

Deficient

2,048 = 2¹¹. It has 12 divisors, adding up to 4,095.

Its divisors, itself excluded, add up to less than the number.

Families it belongs to

Power of two

Two multiplied by itself. Every extra bit doubles it.

Laid out as dots

It fits as 32 × 64. The more divisors, the closer to a square.

Prime factors
2¹¹
Divisors
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
Sum of divisors
4,095
Sum without itself
2,047
Coprime below it
1,024
Digit sum
14
Digital root
5
Roman numeral
MMXLVIII
Binary
100000000000
Octal
4000
Hexadecimal
800
Base 36
1KW
Bits
12 bits
Collatz steps
11 steps · peaks at 2,048
Prime before
2039
Prime after
2053

Numbers either side

How to read this

  • The prime factors are what the number is made of. The count and sum of divisors both follow from them.
  • Add the divisors, take the number away, and you get perfect, abundant or deficient.
  • The length of the binary form is the bit count. 255 taking eight digits is what a byte is.
  • Collatz: halve it if even, triple it and add one if odd. The count is how many moves reach 1.

Frequently asked questions

Q. Is 2,048 a prime number?

No. It breaks down into 2¹¹.

Q. What are the divisors of 2,048?

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 — 12 divisors in all, adding up to 4,095.

Q. How is 2,048 written in binary?

100000000000, which is 12 bits. In hexadecimal it is 800.

Q. How many Collatz steps does 2,048 take?

It reaches 1 in 11, peaking at 2,048 on the way.