10102414400 has 126 divisors (see below), whose sum is σ = 26918237502. Its totient is φ = 3730022400.

The previous prime is 10102414397. The next prime is 10102414423. The reversal of 10102414400 is 441420101.

It can be written as a sum of positive squares in 9 ways, for example, as 5465349184 + 4637065216 = 73928^2 + 68096^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 251720 + ... + 289080.

Almost surely, 2^10102414400 is an apocalyptic number.

10102414400 is a gapful number since it is divisible by the number (10) 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 10102414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13459118751).

10102414400 is an abundant number, since it is smaller than the sum of its proper divisors (16815823102).

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

10102414400 is a wasteful number, since it uses less digits than its factorization.

10102414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 37409 (or 37381 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 17.

Adding to 10102414400 its reverse (441420101), we get a palindrome (10543834501).

The spelling of 10102414400 in words is "ten billion, one hundred two million, four hundred fourteen thousand, four hundred".