106406265708800 has 432 divisors, whose sum is σ = 268256473143120. Its totient is φ = 41781055979520.

The previous prime is 106406265708797. The next prime is 106406265708871. The reversal of 106406265708800 is 8807562604601.

It is a happy number.

It can be written as a sum of positive squares in 24 ways, for example, as 92883642163456 + 13522623545344 = 9637616^2 + 3677312^2 .

It is a super-2 number, since 2×106406265708800² (a number of 29 digits) contains 22 as substring.

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, 103007033084 + ... + 103007034116.

Almost surely, 2^{106406265708800} is an apocalyptic number.

106406265708800 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 106406265708800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134128236571560).

106406265708800 is an abundant number, since it is smaller than the sum of its proper divisors (161850207434320).

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

106406265708800 is a wasteful number, since it uses less digits than its factorization.

106406265708800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2278 (or 2259 counting only the distinct ones).

The product of its (nonzero) digits is 3870720, while the sum is 53.

The spelling of 106406265708800 in words is "one hundred six trillion, four hundred six billion, two hundred sixty-five million, seven hundred eight thousand, eight hundred".