78336 has 60 divisors (see below), whose sum is σ = 239382. Its totient is φ = 24576.

The previous prime is 78317. The next prime is 78341. The reversal of 78336 is 63387.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 57600 + 20736 = 240^2 + 144^2 .

It is a super-3 number, since 3×78336³ = 1442133382791168, which contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is an unprimeable number.

78336 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 4600 + ... + 4616.

2⁷⁸³³⁶ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 78336, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119691).

78336 is an abundant number, since it is smaller than the sum of its proper divisors (161046).

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

78336 is a wasteful number, since it uses less digits than its factorization.

78336 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41 (or 22 counting only the distinct ones).

The product of its digits is 3024, while the sum is 27.

The square root of 78336 is about 279.8856909526. The cubic root of 78336 is about 42.7878499299.

It can be divided in two parts, 78 and 336, that added together give a palindrome (414).

The spelling of 78336 in words is "seventy-eight thousand, three hundred thirty-six".