10506121646400 has 1008 divisors, whose sum is σ = 38840237280000. Its totient is φ = 2692085760000.

The previous prime is 10506121646393. The next prime is 10506121646519. The reversal of 10506121646400 is 464612160501.

10506121646400 is a `hidden beast` number, since 1 + 0 + 5 + 0 + 6 + 1 + 2 + 1 + 6 + 4 + 640 + 0 = 666.

It is a super-2 number, since 2×10506121646400² (a number of 27 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 143 ways as a sum of consecutive naturals, for example, 7008752851 + ... + 7008754349.

Almost surely, 2^{10506121646400} is an apocalyptic number.

10506121646400 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 10506121646400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19420118640000).

10506121646400 is an abundant number, since it is smaller than the sum of its proper divisors (28334115633600).

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

10506121646400 is a wasteful number, since it uses less digits than its factorization.

10506121646400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1768 (or 1750 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 10506121646400 in words is "ten trillion, five hundred six billion, one hundred twenty-one million, six hundred forty-six thousand, four hundred".