83791688288400 has 135 divisors (see below), whose sum is σ = 290782339811769. Its totient is φ = 22344303749760.

The previous prime is 83791688288293. The next prime is 83791688288417. The reversal of 83791688288400 is 488288619738.

The square root of 83791688288400 is 9153780.

It is a perfect power (a square), and thus also a powerful number.

83791688288400 is a `hidden beast` number, since 8 + 3 + 7 + 9 + 1 + 68 + 82 + 88 + 400 = 666.

It can be written as a sum of positive squares in only one way, i.e., 30165007783824 + 53626680504576 = 5492268^2 + 7323024^2 .

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 549150519 + ... + 549303081.

Almost surely, 2^{83791688288400} is an apocalyptic number.

83791688288400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

83791688288400 is the 9153780-th square number.

It is an amenable number.

83791688288400 is an abundant number, since it is smaller than the sum of its proper divisors (206990651523369).

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

83791688288400 is an frugal number, since it uses more digits than its factorization.

83791688288400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 305150 (or 152573 counting only the distinct ones).

The product of its (nonzero) digits is 297271296, while the sum is 72.

The spelling of 83791688288400 in words is "eighty-three trillion, seven hundred ninety-one billion, six hundred eighty-eight million, two hundred eighty-eight thousand, four hundred".