4065414400 has 162 divisors, whose sum is σ = 10413334806. Its totient is φ = 1571328000.

The previous prime is 4065414383. The next prime is 4065414407. The reversal of 4065414400 is 44145604.

It can be written as a sum of positive squares in 3 ways, for example, as 639887616 + 3425526784 = 25296^2 + 58528^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4065414407) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 6150070 + ... + 6150730.

Almost surely, 2^4065414400 is an apocalyptic number.

4065414400 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 4065414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5206667403).

4065414400 is an abundant number, since it is smaller than the sum of its proper divisors (6347920406).

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

4065414400 is an equidigital number, since it uses as much as digits as its factorization.

4065414400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 749 (or 699 counting only the distinct ones).

The product of its (nonzero) digits is 7680, while the sum is 28.

The square root of 4065414400 is about 63760.6022556249. The cubic root of 4065414400 is about 1596.0075459806.

The spelling of 4065414400 in words is "four billion, sixty-five million, four hundred fourteen thousand, four hundred".