Numbers·120
120
CXX
1111000

The number 120 — factors and divisors

Abundant

120 = 2³ × 3 × 5. It has 16 divisors, adding up to 360.

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

Families it belongs to

Triangular

The running total of 1, 2, 3 … — the dots stack into a triangle.

Laid out as dots

It fits as 10 × 12. The more divisors, the closer to a square.

Prime factors
2³ × 3 × 5
Divisors
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Sum of divisors
360
Sum without itself
240
Coprime below it
32
Digit sum
3
Digital root
3
Roman numeral
CXX
Binary
1111000
Octal
170
Hexadecimal
78
Base 36
3C
Bits
7 bits
Collatz steps
20 steps · peaks at 160
Prime before
113
Prime after
127

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 120 a prime number?

No. It breaks down into 2³ × 3 × 5.

Q. What are the divisors of 120?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 — 16 divisors in all, adding up to 360.

Q. How is 120 written in binary?

1111000, which is 7 bits. In hexadecimal it is 78.

Q. How many Collatz steps does 120 take?

It reaches 1 in 20, peaking at 160 on the way.