72193531737600 has 4320 divisors, whose sum is σ = 340465856290560. Its totient is φ = 15014244188160.

The previous prime is 72193531737599. The next prime is 72193531737601. The reversal of 72193531737600 is 673713539127.

72193531737600 is a `hidden beast` number, since 7 + 2 + 19 + 3 + 5 + 3 + 17 + 3 + 7 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (72193531737599) and next prime (72193531737601).

It is a tau number, because it is divible by the number of its divisors (4320).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72193531737601) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 164449958181 + ... + 164449958619.

It is an arithmetic number, because the mean of its divisors is an integer number (78811540808).

Almost surely, 2^{72193531737600} is an apocalyptic number.

72193531737600 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72193531737600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (170232928145280).

72193531737600 is an abundant number, since it is smaller than the sum of its proper divisors (268272324552960).

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

72193531737600 is a wasteful number, since it uses less digits than its factorization.

72193531737600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 592 (or 552 counting only the distinct ones).

The product of its (nonzero) digits is 5000940, while the sum is 54.

The spelling of 72193531737600 in words is "seventy-two trillion, one hundred ninety-three billion, five hundred thirty-one million, seven hundred thirty-seven thousand, six hundred".