3407125305600 has 243 divisors, whose sum is σ = 12182825973409. Its totient is φ = 908448614400.

The previous prime is 3407125305439. The next prime is 3407125305629. The reversal of 3407125305600 is 65035217043.

The square root of 3407125305600 is 1845840.

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

3407125305600 is a `hidden beast` number, since 3 + 4 + 0 + 7 + 12 + 5 + 30 + 5 + 600 = 666.

It can be written as a sum of positive squares in only one way, i.e., 1226565110016 + 2180560195584 = 1107504^2 + 1476672^2 .

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

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 26 ways as a sum of consecutive naturals, for example, 442997755 + ... + 443005445.

Almost surely, 2^{3407125305600} is an apocalyptic number.

3407125305600 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

3407125305600 is the 1845840-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 3407125305600

3407125305600 is an abundant number, since it is smaller than the sum of its proper divisors (8775700667809).

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

3407125305600 is an frugal number, since it uses more digits than its factorization.

3407125305600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 15414 (or 7701 counting only the distinct ones).

The product of its (nonzero) digits is 75600, while the sum is 36.

Multiplying 3407125305600 by its sum of digits (36), we get a square (122656511001600 = 11075040²).

3407125305600 divided by its sum of digits (36) gives a square (94642369600 = 307640²).

The spelling of 3407125305600 in words is "three trillion, four hundred seven billion, one hundred twenty-five million, three hundred five thousand, six hundred".