126505806350400 has 945 divisors, whose sum is σ = 470347690196439. Its totient is φ = 33351567575040.

The previous prime is 126505806350333. The next prime is 126505806350477. The reversal of 126505806350400 is 4053608505621.

The square root of 126505806350400 is 11247480.

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

126505806350400 is a `hidden beast` number, since 1 + 2 + 6 + 5 + 0 + 5 + 8 + 0 + 635 + 0 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 15300176463936 + 111205629886464 = 3911544^2 + 10545408^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 635707569501 + ... + 635707569699.

Almost surely, 2^{126505806350400} is an apocalyptic number.

126505806350400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

126505806350400 is the 11247480-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 126505806350400

126505806350400 is an abundant number, since it is smaller than the sum of its proper divisors (343841883846039).

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

126505806350400 is an frugal number, since it uses more digits than its factorization.

126505806350400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 746 (or 366 counting only the distinct ones).

The product of its (nonzero) digits is 864000, while the sum is 45.

The spelling of 126505806350400 in words is "one hundred twenty-six trillion, five hundred five billion, eight hundred six million, three hundred fifty thousand, four hundred".