101268000 has 288 divisors, whose sum is σ = 375626160. Its totient is φ = 25804800.

The previous prime is 101267993. The next prime is 101268007. The reversal of 101268000 is 862101.

It is an interprime number because it is at equal distance from previous prime (101267993) and next prime (101268007).

It can be written as a sum of positive squares in 8 ways, for example, as 2782224 + 98485776 = 1668^2 + 9924^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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

It is not an unprimeable number, because it can be changed into a prime (101268007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1043952 + ... + 1044048.

Almost surely, 2^101268000 is an apocalyptic number.

101268000 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 101268000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (187813080).

101268000 is an abundant number, since it is smaller than the sum of its proper divisors (274358160).

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

101268000 is a wasteful number, since it uses less digits than its factorization.

101268000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 157 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 18.

The square root of 101268000 is about 10063.2002861913. The cubic root of 101268000 is about 466.1124941010.

The spelling of 101268000 in words is "one hundred one million, two hundred sixty-eight thousand".