1461920400 has 150 divisors (see below), whose sum is σ = 5246831282. Its totient is φ = 389836800.

The previous prime is 1461920393. The next prime is 1461920419. The reversal of 1461920400 is 40291641.

1461920400 is a `hidden beast` number, since 1 + 4 + 619 + 2 + 0 + 40 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 2985984 + 1458934416 = 1728^2 + 38196^2 .

It is a tau number, because it is divible by the number of its divisors (150).

It is a super-2 number, since 2×1461920400² = 4274422511872320000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 9840 + ... + 54960.

Almost surely, 2^1461920400 is an apocalyptic number.

1461920400 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 1461920400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2623415641).

1461920400 is an abundant number, since it is smaller than the sum of its proper divisors (3784910882).

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

1461920400 is a wasteful number, since it uses less digits than its factorization.

1461920400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45151 (or 45131 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 1461920400 is about 38235.0676735376. The cubic root of 1461920400 is about 1134.9443716388.

The spelling of 1461920400 in words is "one billion, four hundred sixty-one million, nine hundred twenty thousand, four hundred".