414314120 has 64 divisors (see below), whose sum is σ = 1027131840. Its totient is φ = 149152000.

The previous prime is 414314119. The next prime is 414314129. The reversal of 414314120 is 21413414.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a junction number, because it is equal to n+sod(n) for n = 414314092 and 414314101.

It is not an unprimeable number, because it can be changed into a prime (414314129) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 39779 + ... + 49101.

It is an arithmetic number, because the mean of its divisors is an integer number (16048935).

Almost surely, 2^414314120 is an apocalyptic number.

414314120 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 414314120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (513565920).

414314120 is an abundant number, since it is smaller than the sum of its proper divisors (612817720).

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

414314120 is a wasteful number, since it uses less digits than its factorization.

414314120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 9446 (or 9442 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 20.

The square root of 414314120 is about 20354.7075636080. The cubic root of 414314120 is about 745.4924420191.

Adding to 414314120 its reverse (21413414), we get a palindrome (435727534).

The spelling of 414314120 in words is "four hundred fourteen million, three hundred fourteen thousand, one hundred twenty".