42008601600 has 891 divisors, whose sum is σ = 177882852771. Its totient is φ = 9444556800.

The previous prime is 42008601581. The next prime is 42008601619. The reversal of 42008601600 is 610680024.

The square root of 42008601600 is 204960.

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

42008601600 is a `hidden beast` number, since 420 + 0 + 86 + 0 + 160 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (42008601581) and next prime (42008601619).

It can be written as a sum of positive squares in 4 ways, for example, as 19349922816 + 22658678784 = 139104^2 + 150528^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 688665570 + ... + 688665630.

Almost surely, 2^42008601600 is an apocalyptic number.

42008601600 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

42008601600 is the 204960-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 42008601600

42008601600 is an abundant number, since it is smaller than the sum of its proper divisors (135874251171).

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

42008601600 is a wasteful number, since it uses less digits than its factorization.

42008601600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 172 (or 78 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

Multiplying 42008601600 by its product of nonzero digits (2304), we get a square (96787818086400 = 9838080²).

42008601600 divided by its product of nonzero digits (2304) gives a square (18232900 = 4270²).

The spelling of 42008601600 in words is "forty-two billion, eight million, six hundred one thousand, six hundred".