102586400 has 108 divisors (see below), whose sum is σ = 291438378. Its totient is φ = 35159040.

The previous prime is 102586391. The next prime is 102586403. The reversal of 102586400 is 4685201.

It can be written as a sum of positive squares in 3 ways, for example, as 97693456 + 4892944 = 9884^2 + 2212^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 102586400.

It is not an unprimeable number, because it can be changed into a prime (102586403) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 37892 + ... + 40508.

Almost surely, 2^102586400 is an apocalyptic number.

102586400 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 102586400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145719189).

102586400 is an abundant number, since it is smaller than the sum of its proper divisors (188851978).

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

102586400 is a wasteful number, since it uses less digits than its factorization.

102586400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2651 (or 2631 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 26.

The square root of 102586400 is about 10128.4944587041. The cubic root of 102586400 is about 468.1265394307.

The spelling of 102586400 in words is "one hundred two million, five hundred eighty-six thousand, four hundred".