101606400 has 495 divisors, whose sum is σ = 437662929. Its totient is φ = 23224320.

The previous prime is 101606389. The next prime is 101606413. The reversal of 101606400 is 4606101.

The square root of 101606400 is 10080.

It is a perfect power (a square), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (7!)² ⋅ (2!)².

101606400 is a `hidden beast` number, since 10 + 16 + 0 + 640 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 36578304 + 65028096 = 6048^2 + 8064^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 14515197 + ... + 14515203.

Almost surely, 2^101606400 is an apocalyptic number.

101606400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

101606400 is the 10080-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 101606400

101606400 is an abundant number, since it is smaller than the sum of its proper divisors (336056529).

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

101606400 is an equidigital number, since it uses as much as digits as its factorization.

101606400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 56 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The cubic root of 101606400 is about 466.6311084018.

Multiplying 101606400 by its product of nonzero digits (144), we get a square (14631321600 = 120960²).

101606400 divided by its product of nonzero digits (144) gives a square (705600 = 840²).

The spelling of 101606400 in words is "one hundred one million, six hundred six thousand, four hundred".