4601461737600 has 4320 divisors, whose sum is σ = 22738438592100. Its totient is φ = 907141939200.

The previous prime is 4601461737581. The next prime is 4601461737617. The reversal of 4601461737600 is 67371641064.

4601461737600 is a `hidden beast` number, since 4 + 6 + 0 + 1 + 4 + 6 + 1 + 7 + 37 + 600 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 908330988096 + 3693130749504 = 953064^2 + 1921752^2 .

It is a tau number, because it is divible by the number of its divisors (4320).

It is a super-3 number, since 3×4601461737600³ (a number of 39 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

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

It is an unprimeable number.

It is a polite number, since it can be written in 539 ways as a sum of consecutive naturals, for example, 148434249585 + ... + 148434249615.

Almost surely, 2^{4601461737600} is an apocalyptic number.

4601461737600 is a gapful number since it is divisible by the number (40) 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 4601461737600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11369219296050).

4601461737600 is an abundant number, since it is smaller than the sum of its proper divisors (18136976854500).

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

4601461737600 is a wasteful number, since it uses less digits than its factorization.

4601461737600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 154 (or 90 counting only the distinct ones).

The product of its (nonzero) digits is 508032, while the sum is 45.

The spelling of 4601461737600 in words is "four trillion, six hundred one billion, four hundred sixty-one million, seven hundred thirty-seven thousand, six hundred".