Number reference
84 explained.
84: eighty-four, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- eighty-four
- Classification
- composite
- Factors
- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Prime factorization
- 2 × 2 × 3 × 7
- Square root
- 9.165151
- Cube root
- 4.379519
- Binary
- 1010100
- Octal
- 124
- Hexadecimal
- 54
- Roman numeral
- LXXXIV
- Digit sum
- 12
- Digital root
- 3
What makes 84 notable
- Factor structure. 84 breaks down into 3 distinct primes (2, 3, 7) and has 12 divisors in total, so it can be split into equal whole-number groups 10 ways beyond 1 and itself.
84 in everyday use
Uranus takes about 84 years to orbit the Sun, so a person who lives to 84 has seen it go round once. Eighty-four is the atomic number of polonium, the element the Curies named after Poland in 1898. George Orwell's Nineteen Eighty-Four gave the year a permanent shadow, and Helene Hanff's 84, Charing Cross Road is a much-loved book of letters to a London bookshop. Eighty-four hours is three and a half days.
Eighty-four is seven dozen, 7 × 12, and a tetrahedral number: 1 + 3 + 6 + 10 + 15 + 21 + 28, the balls in a seven-layer pyramid. It factors as 2² × 3 × 7 and has twelve divisors. It is also the sum of the first seven triangular numbers by definition, and the sum of twin primes 41 + 43. In binary it is 1010100.
Nearby numbers
How to read this page
The factor list shows every way 84 splits into equal whole-number groups — 12 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 84 for contexts that do not use decimal.
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