7540646400 has 600 divisors, whose sum is σ = 31926111360. Its totient is φ = 1721917440.

The previous prime is 7540646389. The next prime is 7540646401. The reversal of 7540646400 is 46460457.

7540646400 is a `hidden beast` number, since 7 + 5 + 4 + 0 + 6 + 4 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (600).

It is a super-2 number, since 2×7540646400² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (7540646401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 7257081 + ... + 7258119.

Almost surely, 2^7540646400 is an apocalyptic number.

7540646400 is a gapful number since it is divisible by the number (70) 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 7540646400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15963055680).

7540646400 is an abundant number, since it is smaller than the sum of its proper divisors (24385464960).

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

7540646400 is a wasteful number, since it uses less digits than its factorization.

7540646400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1086 (or 1056 counting only the distinct ones).

The product of its (nonzero) digits is 80640, while the sum is 36.

The square root of 7540646400 is about 86836.8953843929. The cubic root of 7540646400 is about 1960.9635689756.

The spelling of 7540646400 in words is "seven billion, five hundred forty million, six hundred forty-six thousand, four hundred".