61564737542400 has 243 divisors, whose sum is σ = 220114564306819. Its totient is φ = 16416761180160.

The previous prime is 61564737542381. The next prime is 61564737542419. The reversal of 61564737542400 is 424573746516.

The square root of 61564737542400 is 7846320.

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

61564737542400 is a `hidden beast` number, since 6 + 1 + 5 + 64 + 7 + 37 + 542 + 4 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (61564737542381) and next prime (61564737542419).

It can be written as a sum of positive squares in 4 ways, for example, as 30360805284096 + 31203932258304 = 5510064^2 + 5586048^2 .

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 1883100454 + ... + 1883133146.

Almost surely, 2^{61564737542400} is an apocalyptic number.

61564737542400 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

61564737542400 is the 7846320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 61564737542400

61564737542400 is an abundant number, since it is smaller than the sum of its proper divisors (158549826764419).

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

61564737542400 is an frugal number, since it uses more digits than its factorization.

61564737542400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 65418 (or 32703 counting only the distinct ones).

The product of its (nonzero) digits is 16934400, while the sum is 54.

The spelling of 61564737542400 in words is "sixty-one trillion, five hundred sixty-four billion, seven hundred thirty-seven million, five hundred forty-two thousand, four hundred".