77968100 has 72 divisors (see below), whose sum is σ = 199653888. Its totient is φ = 25862400.

The previous prime is 77968081. The next prime is 77968109. The reversal of 77968100 is 186977.

It is a happy number.

It is a super-2 number, since 2×77968100² = 12158049235220000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (38) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (77968109) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 19904 + ... + 23496.

Almost surely, 2^77968100 is an apocalyptic number.

77968100 is a gapful number since it is divisible by the number (70) 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 77968100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (99826944).

77968100 is an abundant number, since it is smaller than the sum of its proper divisors (121685788).

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

77968100 is a wasteful number, since it uses less digits than its factorization.

77968100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3645 (or 3638 counting only the distinct ones).

The product of its (nonzero) digits is 21168, while the sum is 38.

The square root of 77968100 is about 8829.9546997705. The cubic root of 77968100 is about 427.2076132993.

The spelling of 77968100 in words is "seventy-seven million, nine hundred sixty-eight thousand, one hundred".