642507465600 has 6144 divisors, whose sum is σ = 3671764992000. Its totient is φ = 105106636800.

The previous prime is 642507465571. The next prime is 642507465637. The reversal of 642507465600 is 6564705246.

642507465600 is a `hidden beast` number, since 6 + 42 + 5 + 0 + 7 + 46 + 560 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 767 ways as a sum of consecutive naturals, for example, 27935107189 + ... + 27935107211.

It is an arithmetic number, because the mean of its divisors is an integer number (597618000).

642507465600 is a highly composite number, because it has more divisors than any smaller number.

642507465600 is a superabundant number, because it has a larger abundancy index than any smaller number.

Almost surely, 2^642507465600 is an apocalyptic number.

642507465600 is a gapful number since it is divisible by the number (60) 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 642507465600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1835882496000).

642507465600 is an abundant number, since it is smaller than the sum of its proper divisors (3029257526400).

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

642507465600 is a wasteful number, since it uses less digits than its factorization.

642507465600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 123 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 1209600, while the sum is 45.

The spelling of 642507465600 in words is "six hundred forty-two billion, five hundred seven million, four hundred sixty-five thousand, six hundred".