106077081600 has 1638 divisors, whose sum is σ = 474585966630. Its totient is φ = 23410114560.

The previous prime is 106077081589. The next prime is 106077081623. The reversal of 106077081600 is 6180770601.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 7169347584 + 98907734016 = 84672^2 + 314496^2 .

It is a super-2 number, since 2×106077081600² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 125 ways as a sum of consecutive naturals, for example, 3657830386 + ... + 3657830414.

Almost surely, 2^106077081600 is an apocalyptic number.

106077081600 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 106077081600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (237292983315).

106077081600 is an abundant number, since it is smaller than the sum of its proper divisors (368508885030).

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

106077081600 is an frugal number, since it uses more digits than its factorization.

106077081600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 95 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 14112, while the sum is 36.

The spelling of 106077081600 in words is "one hundred six billion, seventy-seven million, eighty-one thousand, six hundred".