105356265062400 has 1989 divisors, whose sum is σ = 430790374524013. Its totient is φ = 25540912742400.

The previous prime is 105356265062371. The next prime is 105356265062413. The reversal of 105356265062400 is 4260562653501.

The square root of 105356265062400 is 10264320.

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

105356265062400 is a `hidden beast` number, since 1 + 0 + 5 + 3 + 562 + 65 + 0 + 6 + 24 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 37928255422464 + 67428009639936 = 6158592^2 + 8211456^2 .

It is a super-2 number, since 2×105356265062400² (a number of 29 digits) contains 22 as substring.

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

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 116 ways as a sum of consecutive naturals, for example, 9577842278395 + ... + 9577842278405.

Almost surely, 2^{105356265062400} is an apocalyptic number.

105356265062400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105356265062400 is the 10264320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105356265062400

105356265062400 is an abundant number, since it is smaller than the sum of its proper divisors (325434109461613).

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

105356265062400 is an frugal number, since it uses more digits than its factorization.

105356265062400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 100 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 1296000, while the sum is 45.

The spelling of 105356265062400 in words is "one hundred five trillion, three hundred fifty-six billion, two hundred sixty-five million, sixty-two thousand, four hundred".