106138667606400 has 3072 divisors, whose sum is σ = 470353095475200. Its totient is φ = 23029678080000.

The previous prime is 106138667606317. The next prime is 106138667606423. The reversal of 106138667606400 is 4606766831601.

It is a happy number.

106138667606400 is a `hidden beast` number, since 10 + 6 + 13 + 8 + 6 + 6 + 7 + 606 + 4 + 0 + 0 = 666.

It is a super-2 number, since 2×106138667606400² (a number of 29 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 383 ways as a sum of consecutive naturals, for example, 96753570652 + ... + 96753571748.

It is an arithmetic number, because the mean of its divisors is an integer number (153109731600).

Almost surely, 2^{106138667606400} is an apocalyptic number.

106138667606400 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 106138667606400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (235176547737600).

106138667606400 is an abundant number, since it is smaller than the sum of its proper divisors (364214427868800).

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

106138667606400 is a wasteful number, since it uses less digits than its factorization.

106138667606400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1386 (or 1363 counting only the distinct ones).

The product of its (nonzero) digits is 5225472, while the sum is 54.

The spelling of 106138667606400 in words is "one hundred six trillion, one hundred thirty-eight billion, six hundred sixty-seven million, six hundred six thousand, four hundred".