97825442400 has 648 divisors, whose sum is σ = 411124483224. Its totient is φ = 21811507200.

The previous prime is 97825442389. The next prime is 97825442467. The reversal of 97825442400 is 424452879.

97825442400 is a `hidden beast` number, since 9 + 7 + 82 + 544 + 24 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 14461419 + ... + 14468181.

It is an arithmetic number, because the mean of its divisors is an integer number (634451363).

Almost surely, 2^97825442400 is an apocalyptic number.

97825442400 is a gapful number since it is divisible by the number (90) 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 97825442400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (205562241612).

97825442400 is an abundant number, since it is smaller than the sum of its proper divisors (313299040824).

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

97825442400 is a wasteful number, since it uses less digits than its factorization.

97825442400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6844 (or 6821 counting only the distinct ones).

The product of its (nonzero) digits is 645120, while the sum is 45.

It can be divided in two parts, 97825 and 442400, that added together give a square (540225 = 735²).

The spelling of 97825442400 in words is "ninety-seven billion, eight hundred twenty-five million, four hundred forty-two thousand, four hundred".