Numbers·36
36
XXXVI
100100

The number 36 — factors and divisors

Abundant

36 = 2² × 3². It has 9 divisors, adding up to 91.

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

Families it belongs to

Square

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

Triangular

The running total of 1, 2, 3 … — the dots stack into a triangle.

Laid out as dots

It fits as 6 × 6. The more divisors, the closer to a square.

Prime factors
2² × 3²
Divisors
1, 2, 3, 4, 6, 9, 12, 18, 36
Sum of divisors
91
Sum without itself
55
Coprime below it
12
Digit sum
9
Digital root
9
Roman numeral
XXXVI
Binary
100100
Octal
44
Hexadecimal
24
Base 36
10
Bits
6 bits
Collatz steps
21 steps · peaks at 52
Prime before
31
Prime after
37

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 36 a prime number?

No. It breaks down into 2² × 3².

Q. What are the divisors of 36?

1, 2, 3, 4, 6, 9, 12, 18, 36 — 9 divisors in all, adding up to 91.

Q. How is 36 written in binary?

100100, which is 6 bits. In hexadecimal it is 24.

Q. How many Collatz steps does 36 take?

It reaches 1 in 21, peaking at 52 on the way.