1617640000 has 140 divisors (see below), whose sum is σ = 4123401964. Its totient is φ = 628992000.

The previous prime is 1617639973. The next prime is 1617640019. The reversal of 1617640000 is 467161.

It is a happy number.

It can be written as a sum of positive squares in 10 ways, for example, as 384787456 + 1232852544 = 19616^2 + 35112^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 1479454 + ... + 1480546.

Almost surely, 2^1617640000 is an apocalyptic number.

1617640000 is a gapful number since it is divisible by the number (10) 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 1617640000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2061700982).

1617640000 is an abundant number, since it is smaller than the sum of its proper divisors (2505761964).

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

1617640000 is an equidigital number, since it uses as much as digits as its factorization.

1617640000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1162 (or 1137 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 25.

The square root of 1617640000 is about 40219.8955742056. The cubic root of 1617640000 is about 1173.8897011322.

It can be divided in two parts, 16 and 17640000, that multiplied together give a square (282240000 = 16800²).

The spelling of 1617640000 in words is "one billion, six hundred seventeen million, six hundred forty thousand".