106286400 has 378 divisors, whose sum is σ = 422038526. Its totient is φ = 25344000.

The previous prime is 106286393. The next prime is 106286419. The reversal of 106286400 is 4682601.

106286400 is a `hidden beast` number, since 10 + 6 + 2 + 8 + 640 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 278784 + 106007616 = 528^2 + 10296^2 .

It is a super-2 number, since 2×106286400² = 22593597649920000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 1742370 + ... + 1742430.

Almost surely, 2^106286400 is an apocalyptic number.

106286400 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 106286400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (211019263).

106286400 is an abundant number, since it is smaller than the sum of its proper divisors (315752126).

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

106286400 is a wasteful number, since it uses less digits than its factorization.

106286400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 111 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 106286400 is about 10309.5295721968. The cubic root of 106286400 is about 473.6881995765.

The spelling of 106286400 in words is "one hundred six million, two hundred eighty-six thousand, four hundred".