106775884800 has 1320 divisors, whose sum is σ = 452773817496. Its totient is φ = 24631050240.

The previous prime is 106775884777. The next prime is 106775884823. The reversal of 106775884800 is 8488577601.

It is a happy number.

106775884800 is a `hidden beast` number, since 10 + 6 + 7 + 7 + 588 + 48 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (106775884777) and next prime (106775884823).

It can be written as a sum of positive squares in 12 ways, for example, as 48667889664 + 58107995136 = 220608^2 + 241056^2 .

It is a super-2 number, since 2×106775884800² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 458265484 + ... + 458265716.

Almost surely, 2^106775884800 is an apocalyptic number.

106775884800 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 106775884800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (226386908748).

106775884800 is an abundant number, since it is smaller than the sum of its proper divisors (345997932696).

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

106775884800 is a wasteful number, since it uses less digits than its factorization.

106775884800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 305 (or 273 counting only the distinct ones).

The product of its (nonzero) digits is 3010560, while the sum is 54.

The spelling of 106775884800 in words is "one hundred six billion, seven hundred seventy-five million, eight hundred eighty-four thousand, eight hundred".