416429893152 has 1296 divisors, whose sum is σ = 1607448810240. Its totient is φ = 105564985344.

The previous prime is 416429893151. The next prime is 416429893163. The reversal of 416429893152 is 251398924614.

It is a happy number.

416429893152 is a `hidden beast` number, since 416 + 4 + 2 + 98 + 93 + 1 + 52 = 666.

It is a tau number, because it is divible by the number of its divisors (1296).

It is a super-2 number, since 2×416429893152² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (416429893151) by changing a digit.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 1867398513 + ... + 1867398735.

It is an arithmetic number, because the mean of its divisors is an integer number (1240315440).

Almost surely, 2^416429893152 is an apocalyptic number.

416429893152 is a gapful number since it is divisible by the number (42) 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 416429893152, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (803724405120).

416429893152 is an abundant number, since it is smaller than the sum of its proper divisors (1191018917088).

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

416429893152 is a wasteful number, since it uses less digits than its factorization.

416429893152 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 317 (or 277 counting only the distinct ones).

The product of its digits is 3732480, while the sum is 54.

The spelling of 416429893152 in words is "four hundred sixteen billion, four hundred twenty-nine million, eight hundred ninety-three thousand, one hundred fifty-two".