420657600 has 336 divisors, whose sum is σ = 1560185856. Its totient is φ = 98304000.

The previous prime is 420657599. The next prime is 420657607. The reversal of 420657600 is 6756024.

It is a hoax number, since the sum of its digits (30) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (420657607) 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, 1636672 + ... + 1636928.

Almost surely, 2^420657600 is an apocalyptic number.

420657600 is a gapful number since it is divisible by the number (40) 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 420657600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (780092928).

420657600 is an abundant number, since it is smaller than the sum of its proper divisors (1139528256).

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

420657600 is a wasteful number, since it uses less digits than its factorization.

420657600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 324 (or 309 counting only the distinct ones).

The product of its (nonzero) digits is 10080, while the sum is 30.

The square root of 420657600 is about 20509.9390540294. The cubic root of 420657600 is about 749.2778827298.

The spelling of 420657600 in words is "four hundred twenty million, six hundred fifty-seven thousand, six hundred".