Numbers·81
81
LXXXI
1010001

The number 81 — factors and divisors

Deficient

81 = 3⁴. It has 5 divisors, adding up to 121.

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

Families it belongs to

Square

A number times itself — the dots lay out as a square.

Laid out as dots

It fits as 9 × 9. The more divisors, the closer to a square.

Prime factors
3⁴
Divisors
1, 3, 9, 27, 81
Sum of divisors
121
Sum without itself
40
Coprime below it
54
Digit sum
9
Digital root
9
Roman numeral
LXXXI
Binary
1010001
Octal
121
Hexadecimal
51
Base 36
29
Bits
7 bits
Collatz steps
22 steps · peaks at 244
Prime before
79
Prime after
83

The grid

Ten per row, twenty rows. The filled cells are primes — you can see the multiples of 2 and 5 drop out in columns.

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 81 a prime number?

No. It breaks down into 3⁴.

Q. What are the divisors of 81?

1, 3, 9, 27, 81 — 5 divisors in all, adding up to 121.

Q. How is 81 written in binary?

1010001, which is 7 bits. In hexadecimal it is 51.

Q. How many Collatz steps does 81 take?

It reaches 1 in 22, peaking at 244 on the way.