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.
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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.