416978780400 has 1440 divisors, whose sum is σ = 1936067194880. Its totient is φ = 80621568000.

The previous prime is 416978780363. The next prime is 416978780411. The reversal of 416978780400 is 4087879614.

It is a happy number.

416978780400 is a `hidden beast` number, since 4 + 169 + 7 + 8 + 78 + 0 + 400 = 666.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 192955320 + ... + 192957480.

Almost surely, 2^416978780400 is an apocalyptic number.

416978780400 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 416978780400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (968033597440).

416978780400 is an abundant number, since it is smaller than the sum of its proper divisors (1519088414480).

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

416978780400 is a wasteful number, since it uses less digits than its factorization.

416978780400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2255 (or 2241 counting only the distinct ones).

The product of its (nonzero) digits is 2709504, while the sum is 54.

It can be divided in two parts, 416978 and 780400, that added together give a triangular number (1197378 = T₁₅₄₇).

The spelling of 416978780400 in words is "four hundred sixteen billion, nine hundred seventy-eight million, seven hundred eighty thousand, four hundred".