Numbers·222
222
CCXXII
11011110

The number 222 — factors and divisors

Abundant

222 = 2 × 3 × 37. It has 8 divisors, adding up to 456.

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

Laid out as dots

It fits as 6 × 37. The more divisors, the closer to a square.

Prime factors
2 × 3 × 37
Divisors
1, 2, 3, 6, 37, 74, 111, 222
Sum of divisors
456
Sum without itself
234
Coprime below it
72
Digit sum
6
Digital root
6
Roman numeral
CCXXII
Binary
11011110
Octal
336
Hexadecimal
DE
Base 36
66
Bits
8 bits
Collatz steps
70 steps · peaks at 9,232
Prime before
211
Prime after
223

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.

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240

Numbers either side

219220221223224225

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 222 a prime number?

No. It breaks down into 2 × 3 × 37.

Q. What are the divisors of 222?

1, 2, 3, 6, 37, 74, 111, 222 — 8 divisors in all, adding up to 456.

Q. How is 222 written in binary?

11011110, which is 8 bits. In hexadecimal it is DE.

Q. How many Collatz steps does 222 take?

It reaches 1 in 70, peaking at 9,232 on the way.