77616 has 90 divisors (see below), whose sum is σ = 275652. Its totient is φ = 20160.

The previous prime is 77611. The next prime is 77617. The reversal of 77616 is 61677.

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

It is a self number, because there is not a number n which added to its sum of digits gives 77616.

It is not an unprimeable number, because it can be changed into a prime (77611) by changing a digit.

77616 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 7051 + ... + 7061.

2⁷⁷⁶¹⁶ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77616, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137826).

77616 is an abundant number, since it is smaller than the sum of its proper divisors (198036).

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

77616 is a wasteful number, since it uses less digits than its factorization.

77616 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 23 counting only the distinct ones).

The product of its digits is 1764, while the sum is 27.

The square root of 77616 is about 278.5964823899. The cubic root of 77616 is about 42.6563560155.

77616 divided by its product of digits (1764) gives a palindrome (44).

The spelling of 77616 in words is "seventy-seven thousand, six hundred sixteen".