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.