100077120 has 448 divisors, whose sum is σ = 419892480. Its totient is φ = 22394880.

The previous prime is 100077097. The next prime is 100077137. The reversal of 100077120 is 21770001.

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

It is a junction number, because it is equal to n+sod(n) for n = 100077093 and 100077102.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 7698234 + ... + 7698246.

It is an arithmetic number, because the mean of its divisors is an integer number (937260).

Almost surely, 2^100077120 is an apocalyptic number.

100077120 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 100077120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (209946240).

100077120 is an abundant number, since it is smaller than the sum of its proper divisors (319815360).

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

100077120 is an equidigital number, since it uses as much as digits as its factorization.

100077120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 62 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 98, while the sum is 18.

The square root of 100077120 is about 10003.8552568497. The cubic root of 100077120 is about 464.2781724782.

The spelling of 100077120 in words is "one hundred million, seventy-seven thousand, one hundred twenty".