106142400 has 588 divisors, whose sum is σ = 481951792. Its totient is φ = 22394880.

The previous prime is 106142383. The next prime is 106142431. The reversal of 106142400 is 4241601.

106142400 is a `hidden beast` number, since 10 + 614 + 2 + 40 + 0 = 666.

It is a super-2 number, since 2×106142400² = 22532418155520000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 8164794 + ... + 8164806.

Almost surely, 2^106142400 is an apocalyptic number.

106142400 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 106142400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (240975896).

106142400 is an abundant number, since it is smaller than the sum of its proper divisors (375809392).

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

106142400 is an equidigital number, since it uses as much as digits as its factorization.

106142400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 60 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 106142400 is about 10302.5433753030. The cubic root of 106142400 is about 473.4741805714.

The spelling of 106142400 in words is "one hundred six million, one hundred forty-two thousand, four hundred".