4207749638400 has 3645 divisors, whose sum is σ = 20445067953387. Its totient is φ = 850706841600.

The previous prime is 4207749638371. The next prime is 4207749638413. The reversal of 4207749638400 is 48369477024.

The square root of 4207749638400 is 2051280.

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

4207749638400 is a `hidden beast` number, since 4 + 2 + 0 + 77 + 496 + 3 + 84 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 399444224256 + 3808305414144 = 632016^2 + 1951488^2 .

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 404 ways as a sum of consecutive naturals, for example, 113722963182 + ... + 113722963218.

Almost surely, 2^{4207749638400} is an apocalyptic number.

4207749638400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

4207749638400 is the 2051280-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4207749638400

4207749638400 is an abundant number, since it is smaller than the sum of its proper divisors (16237318314987).

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

4207749638400 is a wasteful number, since it uses less digits than its factorization.

4207749638400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 148 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 8128512, while the sum is 54.

The spelling of 4207749638400 in words is "four trillion, two hundred seven billion, seven hundred forty-nine million, six hundred thirty-eight thousand, four hundred".