106272000 has 360 divisors, whose sum is σ = 405116712. Its totient is φ = 27648000.

The previous prime is 106271993. The next prime is 106272007. The reversal of 106272000 is 272601.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (106271993) and next prime (106272007).

It can be written as a sum of positive squares in 4 ways, for example, as 23970816 + 82301184 = 4896^2 + 9072^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×106272000² = 22587475968000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (106272007) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 2591980 + ... + 2592020.

Almost surely, 2^106272000 is an apocalyptic number.

106272000 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 106272000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202558356).

106272000 is an abundant number, since it is smaller than the sum of its proper divisors (298844712).

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

106272000 is an frugal number, since it uses more digits than its factorization.

106272000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 84 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 18.

The square root of 106272000 is about 10308.8311655590. The cubic root of 106272000 is about 473.6668063781. Note that the first 3 decimals are identical.

The spelling of 106272000 in words is "one hundred six million, two hundred seventy-two thousand".