31
XXXI
11111
The number 31 — factors and divisors
Deficient
31 is a prime: only 1 and itself divide it. The prime before is 29, the next is 37.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
Prime
Nothing divides it but 1 and itself.
Laid out as dots
It only fits in one row. Having no other rectangle is what being prime means.
- Prime factors
- It does not break down further
- Divisors
- 1, 31
- Sum of divisors
- 32
- Sum without itself
- 1
- Coprime below it
- 30
- Digit sum
- 4
- Digital root
- 4
- Roman numeral
- XXXI
- Binary
- 11111
- Octal
- 37
- Hexadecimal
- 1F
- Base 36
- V
- Bits
- 5 bits
- Collatz steps
- 106 steps · peaks at 9,232
- Prime before
- 29
- 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.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200
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 31 a prime number?
Yes. Nothing divides it but 1 and itself.
Q. What are the divisors of 31?
1, 31 — 2 divisors in all, adding up to 32.
Q. How is 31 written in binary?
11111, which is 5 bits. In hexadecimal it is 1F.
Q. How many Collatz steps does 31 take?
It reaches 1 in 106, peaking at 9,232 on the way.