Numbers·54
54
LIV
110110

The number 54 — factors and divisors

Abundant

54 = 2 × 3³. It has 8 divisors, adding up to 120.

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

Laid out as dots

It fits as 6 × 9. The more divisors, the closer to a square.

Prime factors
2 × 3³
Divisors
1, 2, 3, 6, 9, 18, 27, 54
Sum of divisors
120
Sum without itself
66
Coprime below it
18
Digit sum
9
Digital root
9
Roman numeral
LIV
Binary
110110
Octal
66
Hexadecimal
36
Base 36
1I
Bits
6 bits
Collatz steps
112 steps · peaks at 9,232
Prime before
53
Prime after
59

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 54 a prime number?

No. It breaks down into 2 × 3³.

Q. What are the divisors of 54?

1, 2, 3, 6, 9, 18, 27, 54 — 8 divisors in all, adding up to 120.

Q. How is 54 written in binary?

110110, which is 6 bits. In hexadecimal it is 36.

Q. How many Collatz steps does 54 take?

It reaches 1 in 112, peaking at 9,232 on the way.