970829916638400 has 5040 divisors, whose sum is σ = 4745425415334912. Its totient is φ = 192297369600000.

The previous prime is 970829916638339. The next prime is 970829916638459. The reversal of 970829916638400 is 4836619928079.

970829916638400 is a `hidden beast` number, since 9 + 7 + 0 + 8 + 29 + 9 + 166 + 38 + 400 = 666.

970829916638400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (5040).

It is a super-3 number, since 3×970829916638400³ (a number of 46 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a polite number, since it can be written in 719 ways as a sum of consecutive naturals, for example, 843466477825 + ... + 843466478975.

Almost surely, 2^{970829916638400} is an apocalyptic number.

970829916638400 is a gapful number since it is divisible by the number (90) 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 970829916638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2372712707667456).

970829916638400 is an abundant number, since it is smaller than the sum of its proper divisors (3774595498696512).

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

970829916638400 is a wasteful number, since it uses less digits than its factorization.

970829916638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1830 (or 1799 counting only the distinct ones).

The product of its (nonzero) digits is 282175488, while the sum is 72.

The spelling of 970829916638400 in words is "nine hundred seventy trillion, eight hundred twenty-nine billion, nine hundred sixteen million, six hundred thirty-eight thousand, four hundred".