• 84 can be written using four 4's:

84 has 12 divisors (see below), whose sum is σ = 224. Its totient is φ = 24.

The previous prime is 83. The next prime is 89. The reversal of 84 is 48.

84 = T_{1} + T_{2} + ... +
T_{7}.

84 is nontrivially palindromic in base 11 and base 13.

84 is an esthetic number in base 16, because in such base its adjacent digits differ by 1.

84 is a nontrivial binomial coefficient, being equal to C(9, 3).

It is a tau number, because it is divible by the number of its divisors (12).

84 is an admirable number.

It is a hoax number, since the sum of its digits (12) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (12), and also a Moran number because the ratio is a prime number: 7 = 84 / (8 + 4).

It is a O'Halloran number.

84 is a nontrivial repdigit in base 11 and base 13.

It is a plaindrome in base 8, base 11, base 13 and base 15.

It is a nialpdrome in base 4, base 6, base 10, base 11, base 12, base 13, base 14 and base 16.

It is a zygodrome in base 11 and base 13.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 84.

It is the 7-th tetrahedral number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 9 + ... + 15.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 84, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (112).

84 is an abundant number, since it is smaller than the sum of its proper divisors (140).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

84 is a wasteful number, since it uses less digits than its factorization.

84 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 14 (or 12 counting only the distinct ones).

The product of its digits is 32, while the sum is 12.

The square root of 84 is about 9.1651513899. The cubic root of 84 is about 4.3795191399.

Subtracting from 84 its reverse (48), we obtain a triangular number (36 = T_{8}).

The spelling of 84 in words is "eighty-four", and thus it is an aban number.

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