32768
Only up to 3999
1000000000000000
The number 32768 — factors and divisors
Deficient
32,768 = 2¹⁵. It has 16 divisors, adding up to 65,535.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
Cube
A number times itself three times — the dots stack into a cube.
Power of two
Two multiplied by itself. Every extra bit doubles it.
Laid out as dots
It fits as 128 × 256. The more divisors, the closer to a square.
- Prime factors
- 2¹⁵
- Divisors
- 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
- Sum of divisors
- 65,535
- Sum without itself
- 32,767
- Coprime below it
- 16,384
- Digit sum
- 26
- Digital root
- 8
- Roman numeral
- Only up to 3999
- Binary
- 1000000000000000
- Octal
- 100000
- Hexadecimal
- 8000
- Base 36
- PA8
- Bits
- 16 bits
- Collatz steps
- 15 steps · peaks at 32,768
- Prime before
- 32749
- Prime after
- 32771
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 32,768 a prime number?
No. It breaks down into 2¹⁵.
Q. What are the divisors of 32,768?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768 — 16 divisors in all, adding up to 65,535.
Q. How is 32,768 written in binary?
1000000000000000, which is 16 bits. In hexadecimal it is 8000.
Q. How many Collatz steps does 32,768 take?
It reaches 1 in 15, peaking at 32,768 on the way.