106766400 has 336 divisors, whose sum is σ = 396849600. Its totient is φ = 24944640.

The previous prime is 106766399. The next prime is 106766417. The reversal of 106766400 is 4667601.

It is a super-2 number, since 2×106766400² = 22798128337920000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1809571 + ... + 1809629.

It is an arithmetic number, because the mean of its divisors is an integer number (1181100).

Almost surely, 2^106766400 is an apocalyptic number.

106766400 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 106766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (198424800).

106766400 is an abundant number, since it is smaller than the sum of its proper divisors (290083200).

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

106766400 is a wasteful number, since it uses less digits than its factorization.

106766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 126 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 6048, while the sum is 30.

The square root of 106766400 is about 10332.7827810324. The cubic root of 106766400 is about 474.4002032329.

The spelling of 106766400 in words is "one hundred six million, seven hundred sixty-six thousand, four hundred".