103612416000 has 640 divisors, whose sum is σ = 376883020800. Its totient is φ = 25165824000.

The previous prime is 103612415981. The next prime is 103612416023. The reversal of 103612416000 is 614216301.

It is a tau number, because it is divible by the number of its divisors (640).

It is a super-3 number, since 3×103612416000³ (a number of 34 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 3342335985 + ... + 3342336015.

It is an arithmetic number, because the mean of its divisors is an integer number (588879720).

Almost surely, 2^103612416000 is an apocalyptic number.

103612416000 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 103612416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188441510400).

103612416000 is an abundant number, since it is smaller than the sum of its proper divisors (273270604800).

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

103612416000 is an frugal number, since it uses more digits than its factorization.

103612416000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 104 (or 58 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The spelling of 103612416000 in words is "one hundred three billion, six hundred twelve million, four hundred sixteen thousand".