105315211782400 has 243 divisors, whose sum is σ = 267984489176859. Its totient is φ = 40975719690240.

The previous prime is 105315211782383. The next prime is 105315211782401. The reversal of 105315211782400 is 4287112513501.

The square root of 105315211782400 is 10262320.

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

It can be written as a sum of positive squares in 4 ways, for example, as 9997636905216 + 95317574877184 = 3161904^2 + 9763072^2 .

It is a super-2 number, since 2×105315211782400² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is not an unprimeable number, because it can be changed into a prime (105315211782401) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 30376465467 + ... + 30376468933.

Almost surely, 2^{105315211782400} is an apocalyptic number.

105315211782400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105315211782400 is the 10262320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105315211782400

105315211782400 is an abundant number, since it is smaller than the sum of its proper divisors (162669277394459).

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

105315211782400 is an frugal number, since it uses more digits than its factorization.

105315211782400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7034 (or 3511 counting only the distinct ones).

The product of its (nonzero) digits is 67200, while the sum is 40.

The spelling of 105315211782400 in words is "one hundred five trillion, three hundred fifteen billion, two hundred eleven million, seven hundred eighty-two thousand, four hundred".