409735680 has 160 divisors (see below), whose sum is σ = 1352913408. Its totient is φ = 105676800.

The previous prime is 409735583. The next prime is 409735723. The reversal of 409735680 is 86537904.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (160).

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 237220 + ... + 238940.

Almost surely, 2^409735680 is an apocalyptic number.

409735680 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 409735680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (676456704).

409735680 is an abundant number, since it is smaller than the sum of its proper divisors (943177728).

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

409735680 is a wasteful number, since it uses less digits than its factorization.

409735680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1778 (or 1762 counting only the distinct ones).

The product of its (nonzero) digits is 181440, while the sum is 42.

The square root of 409735680 is about 20241.9287618547. The cubic root of 409735680 is about 742.7362057281.

The spelling of 409735680 in words is "four hundred nine million, seven hundred thirty-five thousand, six hundred eighty".