414378720 has 384 divisors, whose sum is σ = 1689569280. Its totient is φ = 92897280.

The previous prime is 414378703. The next prime is 414378737. The reversal of 414378720 is 27873414.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (414378703) and next prime (414378737).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 2146944 + ... + 2147136.

It is an arithmetic number, because the mean of its divisors is an integer number (4399920).

Almost surely, 2^414378720 is an apocalyptic number.

414378720 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 414378720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (844784640).

414378720 is an abundant number, since it is smaller than the sum of its proper divisors (1275190560).

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

414378720 is a wasteful number, since it uses less digits than its factorization.

414378720 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 295 (or 281 counting only the distinct ones).

The product of its (nonzero) digits is 37632, while the sum is 36.

The square root of 414378720 is about 20356.2943582569. The cubic root of 414378720 is about 745.5311858182.

The spelling of 414378720 in words is "four hundred fourteen million, three hundred seventy-eight thousand, seven hundred twenty".