7825838400900 has 567 divisors, whose sum is σ = 27605326056861. Its totient is φ = 1923943207680.

The previous prime is 7825838400881. The next prime is 7825838400929. The reversal of 7825838400900 is 90048385287.

It is a happy number.

The square root of 7825838400900 is 2797470.

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

7825838400900 is a `hidden beast` number, since 7 + 8 + 258 + 384 + 0 + 0 + 9 + 0 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 7391536312644 + 434302088256 = 2718738^2 + 659016^2 .

It is a super-2 number, since 2×7825838400900² (a number of 27 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 9819119302 + ... + 9819120098.

Almost surely, 2^{7825838400900} is an apocalyptic number.

7825838400900 is the 2797470-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7825838400900

7825838400900 is an abundant number, since it is smaller than the sum of its proper divisors (19779487655961).

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

7825838400900 is an equidigital number, since it uses as much as digits as its factorization.

7825838400900 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1652 (or 820 counting only the distinct ones).

The product of its (nonzero) digits is 3870720, while the sum is 54.

The spelling of 7825838400900 in words is "seven trillion, eight hundred twenty-five billion, eight hundred thirty-eight million, four hundred thousand, nine hundred".