1972100 has 72 divisors (see below), whose sum is σ = 4848648. Its totient is φ = 691200.

The previous prime is 1972099. The next prime is 1972111. The reversal of 1972100 is 12791.

1972100 = T₂₄₉ + T₂₅₀ + ... + T₃₀₀.

It can be written as a sum of positive squares in 12 ways, for example, as 984064 + 988036 = 992^2 + 994^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 48080 + ... + 48120.

2^1972100 is an apocalyptic number.

1972100 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 1972100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2424324).

1972100 is an abundant number, since it is smaller than the sum of its proper divisors (2876548).

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

1972100 is a wasteful number, since it uses less digits than its factorization.

1972100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 105 (or 98 counting only the distinct ones).

The product of its (nonzero) digits is 126, while the sum is 20.

The square root of 1972100 is about 1404.3147795277. The cubic root of 1972100 is about 125.4034961256.

Adding to 1972100 its reverse (12791), we get a palindrome (1984891).

The spelling of 1972100 in words is "one million, nine hundred seventy-two thousand, one hundred".