7465900464400 has 405 divisors, whose sum is σ = 21641747043501. Its totient is φ = 2467798179840.

The previous prime is 7465900464389. The next prime is 7465900464413. The reversal of 7465900464400 is 44640095647.

It is a happy number.

The square root of 7465900464400 is 2732380.

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

It can be written as a sum of positive squares in 13 ways, for example, as 5802914837776 + 1662985626624 = 2408924^2 + 1289568^2 .

It is a Harshad number since it is a multiple of its sum of digits (49).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 11093462464 + ... + 11093463136.

Almost surely, 2^{7465900464400} is an apocalyptic number.

7465900464400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

7465900464400 is the 2732380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7465900464400

7465900464400 is an abundant number, since it is smaller than the sum of its proper divisors (14175846579101).

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

7465900464400 is an equidigital number, since it uses as much as digits as its factorization.

7465900464400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1436 (or 716 counting only the distinct ones).

The product of its (nonzero) digits is 2903040, while the sum is 49.

Multiplying 7465900464400 by its sum of digits (49), we get a square (365829122755600 = 19126660²).

7465900464400 divided by its sum of digits (49) gives a square (152365315600 = 390340²).

The spelling of 7465900464400 in words is "seven trillion, four hundred sixty-five billion, nine hundred million, four hundred sixty-four thousand, four hundred".