101646400 has 168 divisors, whose sum is σ = 274676616. Its totient is φ = 36864000.

The previous prime is 101646343. The next prime is 101646401. The reversal of 101646400 is 4646101.

It can be written as a sum of positive squares in 12 ways, for example, as 1806336 + 99840064 = 1344^2 + 9992^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101646401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1006350 + ... + 1006450.

Almost surely, 2^101646400 is an apocalyptic number.

101646400 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 101646400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137338308).

101646400 is an abundant number, since it is smaller than the sum of its proper divisors (173030216).

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

101646400 is a wasteful number, since it uses less digits than its factorization.

101646400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 177 (or 162 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The square root of 101646400 is about 10081.9839317468. The cubic root of 101646400 is about 466.6923341891.

It can be divided in two parts, 101 and 646400, that multiplied together give a square (65286400 = 8080²).

The spelling of 101646400 in words is "one hundred one million, six hundred forty-six thousand, four hundred".