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.
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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.