Numbers·19
19
XIX
10011

The number 19 — factors and divisors

Deficient

19 is a prime: only 1 and itself divide it. The prime before is 17, the next is 23.

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, 19
Sum of divisors
20
Sum without itself
1
Coprime below it
18
Digit sum
10
Digital root
1
Roman numeral
XIX
Binary
10011
Octal
23
Hexadecimal
13
Base 36
J
Bits
5 bits
Collatz steps
20 steps · peaks at 88
Prime before
17
Prime after
23

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 19 a prime number?

Yes. Nothing divides it but 1 and itself.

Q. What are the divisors of 19?

1, 19 — 2 divisors in all, adding up to 20.

Q. How is 19 written in binary?

10011, which is 5 bits. In hexadecimal it is 13.

Q. How many Collatz steps does 19 take?

It reaches 1 in 20, peaking at 88 on the way.