419493960 has 192 divisors, whose sum is σ = 1415821680. Its totient is φ = 107642880.

The previous prime is 419493947. The next prime is 419493973. The reversal of 419493960 is 69394914.

It is an interprime number because it is at equal distance from previous prime (419493947) and next prime (419493973).

It can be written as a sum of positive squares in 8 ways, for example, as 166874724 + 252619236 = 12918^2 + 15894^2 .

It is a hoax number, since the sum of its digits (45) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1431574 + ... + 1431866.

Almost surely, 2^419493960 is an apocalyptic number.

419493960 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 419493960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (707910840).

419493960 is an abundant number, since it is smaller than the sum of its proper divisors (996327720).

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

419493960 is a wasteful number, since it uses less digits than its factorization.

419493960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 448 (or 441 counting only the distinct ones).

The product of its (nonzero) digits is 209952, while the sum is 45.

The square root of 419493960 is about 20481.5516990291. The cubic root of 419493960 is about 748.5863504674.

The spelling of 419493960 in words is "four hundred nineteen million, four hundred ninety-three thousand, nine hundred sixty".