414342720 has 504 divisors, whose sum is σ = 1660047480. Its totient is φ = 94617600.

The previous prime is 414342701. The next prime is 414342743. The reversal of 414342720 is 27243414.

It can be written as a sum of positive squares in 4 ways, for example, as 1115136 + 413227584 = 1056^2 + 20328^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 10105900 + ... + 10105940.

It is an arithmetic number, because the mean of its divisors is an integer number (3293745).

Almost surely, 2^414342720 is an apocalyptic number.

414342720 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 414342720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (830023740).

414342720 is an abundant number, since it is smaller than the sum of its proper divisors (1245704760).

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

414342720 is a wasteful number, since it uses less digits than its factorization.

414342720 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 115 (or 91 counting only the distinct ones).

The product of its (nonzero) digits is 5376, while the sum is 27.

The square root of 414342720 is about 20355.4100916685. The cubic root of 414342720 is about 745.5095953433.

The spelling of 414342720 in words is "four hundred fourteen million, three hundred forty-two thousand, seven hundred twenty".