416779678679040 has 1280 divisors, whose sum is σ = 1545651258624000. Its totient is φ = 107330226094080.

The previous prime is 416779678678991. The next prime is 416779678679107. The reversal of 416779678679040 is 40976876977614.

It is a happy number.

416779678679040 is a `hidden beast` number, since 416 + 7 + 7 + 9 + 6 + 78 + 6 + 7 + 90 + 40 = 666.

It is a tau number, because it is divible by the number of its divisors (1280).

It is a super-3 number, since 3×416779678679040³ (a number of 45 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (81).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 295798209856 + ... + 295798211264.

It is an arithmetic number, because the mean of its divisors is an integer number (1207540045800).

Almost surely, 2^{416779678679040} is an apocalyptic number.

416779678679040 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 416779678679040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (772825629312000).

416779678679040 is an abundant number, since it is smaller than the sum of its proper divisors (1128871579944960).

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

416779678679040 is an equidigital number, since it uses as much as digits as its factorization.

416779678679040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2206 (or 2169 counting only the distinct ones).

The product of its (nonzero) digits is 5377010688, while the sum is 81.

The spelling of 416779678679040 in words is "four hundred sixteen trillion, seven hundred seventy-nine billion, six hundred seventy-eight million, six hundred seventy-nine thousand, forty".