Number analysis
84
84 is a composite even number that factors as 2^2 × 3 × 7.
84 is a composite even number that factors as 2^2 × 3 × 7.
The number itself
- Value
- 84
- Digits
- 2
- Digit sum
- 12
- Reversed
- 48
- Palindrome
- No
8 + 4
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 48.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^2 × 3 × 7
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 83 ← → 89
Divisible by 2.
Composite — it factors as 2^2 × 3 × 7.
3 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 6 between them.
Divisors
- Aliquot sum
- 140
- Classification
- Abundant
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The proper divisors — everything except n itself.
Its proper divisors overshoot by 56.
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
- 5 + 79
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
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 9 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 12 — 84 ÷ 12 = 7.
Peaks at 84 along the way.
Written other ways
- Binary
- 1010100
- Octal
- 124
- Hexadecimal
- 54
- Base 36
- 2C
- Roman numerals
- LXXXIV
- In words
- eighty-four
- Scientific notation
- 8.4 × 10^1
Is 84 a prime number?
Composite — it factors as 2^2 × 3 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 84 their own way.
- Greek (alphabetic)
- ΠΔʹ
- Babylonian cuneiform
- 𒐕𒎙𒐘
- Tamil
- ௮௰௪
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.