106972128 has 144 divisors (see below), whose sum is σ = 324913680. Its totient is φ = 33288192.

The previous prime is 106972121. The next prime is 106972139. The reversal of 106972128 is 821279601.

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×106972128² = 22886072337696768, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 106972092 and 106972101.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (106972121) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 618250 + ... + 618422.

It is an arithmetic number, because the mean of its divisors is an integer number (2256345).

Almost surely, 2^106972128 is an apocalyptic number.

106972128 is a gapful number since it is divisible by the number (18) 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 106972128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (162456840).

106972128 is an abundant number, since it is smaller than the sum of its proper divisors (217941552).

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

106972128 is a wasteful number, since it uses less digits than its factorization.

106972128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 321 (or 310 counting only the distinct ones).

The product of its (nonzero) digits is 12096, while the sum is 36.

The square root of 106972128 is about 10342.7331010715. The cubic root of 106972128 is about 474.7047147186.

The spelling of 106972128 in words is "one hundred six million, nine hundred seventy-two thousand, one hundred twenty-eight".