4133414286400 has 567 divisors, whose sum is σ = 12147425457069. Its totient is φ = 1380282408960.

The previous prime is 4133414286383. The next prime is 4133414286511. The reversal of 4133414286400 is 46824143314.

It is a happy number.

The square root of 4133414286400 is 2033080.

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

It can be written as a sum of positive squares in 13 ways, for example, as 1358977725504 + 2774436560896 = 1165752^2 + 1665664^2 .

It is a super-2 number, since 2×4133414286400² (a number of 26 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 30170907132 + ... + 30170907268.

Almost surely, 2^{4133414286400} is an apocalyptic number.

4133414286400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

4133414286400 is the 2033080-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4133414286400

4133414286400 is an abundant number, since it is smaller than the sum of its proper divisors (8014011170669).

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

4133414286400 is an equidigital number, since it uses as much as digits as its factorization.

4133414286400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 416 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 40.

The spelling of 4133414286400 in words is "four trillion, one hundred thirty-three billion, four hundred fourteen million, two hundred eighty-six thousand, four hundred".