31535075672100 has 3645 divisors, whose sum is σ = 145488322418985. Its totient is φ = 5692880793600.

The previous prime is 31535075672071. The next prime is 31535075672197. The reversal of 31535075672100 is 127657053513.

The square root of 31535075672100 is 5615610.

It is a perfect power (a square), and thus also a powerful number.

31535075672100 is a `hidden beast` number, since 3 + 1 + 535 + 0 + 7 + 5 + 6 + 7 + 2 + 100 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 22966388490276 + 8568687181824 = 4792326^2 + 2927232^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 1214 ways as a sum of consecutive naturals, for example, 1855004451292 + ... + 1855004451308.

Almost surely, 2^{31535075672100} is an apocalyptic number.

31535075672100 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

31535075672100 is the 5615610-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 31535075672100

31535075672100 is an abundant number, since it is smaller than the sum of its proper divisors (113953246746885).

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

31535075672100 is a wasteful number, since it uses less digits than its factorization.

31535075672100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 138 (or 58 counting only the distinct ones).

The product of its (nonzero) digits is 661500, while the sum is 45.

The spelling of 31535075672100 in words is "thirty-one trillion, five hundred thirty-five billion, seventy-five million, six hundred seventy-two thousand, one hundred".