66312 has 32 divisors (see below), whose sum is σ = 184800. Its totient is φ = 22032.

The previous prime is 66301. The next prime is 66337. The reversal of 66312 is 21366.

It is a happy number.

66312 is a `hidden beast` number, since 663 + 1 + 2 = 666.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a plaindrome in base 15.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 63 + ... + 369.

It is an arithmetic number, because the mean of its divisors is an integer number (5775).

2⁶⁶³¹² 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 66312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (92400).

66312 is an abundant number, since it is smaller than the sum of its proper divisors (118488).

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

66312 is a wasteful number, since it uses less digits than its factorization.

66312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 322 (or 312 counting only the distinct ones).

The product of its digits is 216, while the sum is 18.

The square root of 66312 is about 257.5111648065. The cubic root of 66312 is about 40.4759802702.

Adding to 66312 its reverse (21366), we get a palindrome (87678).

It can be divided in two parts, 66 and 312, that added together give a triangular number (378 = T₂₇).

The spelling of 66312 in words is "sixty-six thousand, three hundred twelve".