9
IX
1001
The number 9 — factors and divisors
Deficient
9 = 3². It has 3 divisors, adding up to 13.
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 3 × 3. The more divisors, the closer to a square.
- Prime factors
- 3²
- Divisors
- 1, 3, 9
- Sum of divisors
- 13
- Sum without itself
- 4
- Coprime below it
- 6
- Digit sum
- 9
- Digital root
- 9
- Roman numeral
- IX
- Binary
- 1001
- Octal
- 11
- Hexadecimal
- 9
- Base 36
- 9
- Bits
- 4 bits
- Collatz steps
- 19 steps · peaks at 52
- Prime before
- 7
- Prime after
- 11
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 9 a prime number?
No. It breaks down into 3².
Q. What are the divisors of 9?
1, 3, 9 — 3 divisors in all, adding up to 13.
Q. How is 9 written in binary?
1001, which is 4 bits. In hexadecimal it is 9.
Q. How many Collatz steps does 9 take?
It reaches 1 in 19, peaking at 52 on the way.