105777672 has 384 divisors, whose sum is σ = 392999040. Its totient is φ = 23224320.

The previous prime is 105777671. The next prime is 105777691. The reversal of 105777672 is 276777501.

It is a happy number.

It is a super-2 number, since 2×105777672² = 22377831787479168, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (42).

It is not an unprimeable number, because it can be changed into a prime (105777671) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 2858838 + ... + 2858874.

It is an arithmetic number, because the mean of its divisors is an integer number (1023435).

Almost surely, 2^105777672 is an apocalyptic number.

105777672 is a gapful number since it is divisible by the number (12) 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 105777672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196499520).

105777672 is an abundant number, since it is smaller than the sum of its proper divisors (287221368).

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

105777672 is a wasteful number, since it uses less digits than its factorization.

105777672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 101 (or 90 counting only the distinct ones).

The product of its (nonzero) digits is 144060, while the sum is 42.

The square root of 105777672 is about 10284.8272712768. The cubic root of 105777672 is about 472.9312386729.

It can be divided in two parts, 105 and 777672, that added together give a palindrome (777777).

The spelling of 105777672 in words is "one hundred five million, seven hundred seventy-seven thousand, six hundred seventy-two".