414632960 has 176 divisors, whose sum is σ = 1188504576. Its totient is φ = 135708672.

The previous prime is 414632957. The next prime is 414632963. The reversal of 414632960 is 69236414.

It is an interprime number because it is at equal distance from previous prime (414632957) and next prime (414632963).

It is a Harshad number since it is a multiple of its sum of digits (35).

It is a self number, because there is not a number n which added to its sum of digits gives 414632960.

It is not an unprimeable number, because it can be changed into a prime (414632963) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 824069 + ... + 824571.

Almost surely, 2^414632960 is an apocalyptic number.

414632960 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 414632960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (594252288).

414632960 is an abundant number, since it is smaller than the sum of its proper divisors (773871616).

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

414632960 is a wasteful number, since it uses less digits than its factorization.

414632960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 558 (or 540 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 35.

The square root of 414632960 is about 20362.5381522049. The cubic root of 414632960 is about 745.6836269613.

The spelling of 414632960 in words is "four hundred fourteen million, six hundred thirty-two thousand, nine hundred sixty".