102414400 has 189 divisors, whose sum is σ = 289562413. Its totient is φ = 35622400.

The previous prime is 102414373. The next prime is 102414407. The reversal of 102414400 is 4414201.

The square root of 102414400 is 10120.

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

It can be written as a sum of positive squares in only one way, i.e., 36869184 + 65545216 = 6072^2 + 8096^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (102414407) 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, 4452789 + ... + 4452811.

Almost surely, 2^102414400 is an apocalyptic number.

102414400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

102414400 is the 10120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 102414400

102414400 is an abundant number, since it is smaller than the sum of its proper divisors (187148013).

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

102414400 is a wasteful number, since it uses less digits than its factorization.

102414400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 90 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

The cubic root of 102414400 is about 467.8647672192.

Multiplying 102414400 by its sum of digits (16), we get a square (1638630400 = 40480²).

102414400 divided by its sum of digits (16) gives a square (6400900 = 2530²).

Adding to 102414400 its reverse (4414201), we get a palindrome (106828601).

Multiplying 102414400 by its reverse (4414201), we get a square (452077746894400 = 21262120²).

It can be divided in two parts, 10241 and 4400, that added together give a palindrome (14641).

The spelling of 102414400 in words is "one hundred two million, four hundred fourteen thousand, four hundred".