Numbers·32768
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.