Number analysis
120
120 is a composite even number that factors as 2^3 × 3 × 5.
120 is a composite even number that factors as 2^3 × 3 × 5.
The number itself
- Value
- 120
- Digits
- 3
- Digit sum
- 3
- Reversed
- 21
- Palindrome
- No
1 + 2 + 0
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 21.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^3 × 3 × 5
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 113 ← → 127
Divisible by 2.
Composite — it factors as 2^3 × 3 × 5.
3 distinct prime factors, 5 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 14 between them.
Divisors
- Aliquot sum
- 240
- Classification
- Abundant
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The proper divisors — everything except n itself.
Its proper divisors overshoot by 120.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Goldbach pair
- 7 + 113
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Triangular number
- Yes — the 15th
- Hexagonal number
- Yes — the 8th
- Factorial
- Yes — 5!
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 20 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 3 — 120 ÷ 3 = 40.
Peaks at 160 along the way.
Written other ways
- Binary
- 1111000
- Octal
- 170
- Hexadecimal
- 78
- Base 36
- 3C
- Roman numerals
- CXX
- In words
- one hundred and twenty
- Scientific notation
- 1.20 × 10^2
Is 120 a prime number?
Composite — it factors as 2^3 × 3 × 5.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 120 their own way.
- Morse code
- · − − − − · · − − − − − − − −
- Devanagari
- १२०
- Tamil
- ௱௨௰
- Thai
- ๑๒๐
References
Further reading: Wikipedia · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.