420735264768 has 960 divisors, whose sum is σ = 1582285985280. Its totient is φ = 108419088384.

The previous prime is 420735264767. The next prime is 420735264769. The reversal of 420735264768 is 867462537024.

420735264768 is a `hidden beast` number, since 4 + 2 + 0 + 73 + 526 + 47 + 6 + 8 = 666.

It is an interprime number because it is at equal distance from previous prime (420735264767) and next prime (420735264769).

It is a super-3 number, since 3×420735264768³ (a number of 36 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (420735264767) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 709502680 + ... + 709503272.

It is an arithmetic number, because the mean of its divisors is an integer number (1648214568).

Almost surely, 2^420735264768 is an apocalyptic number.

420735264768 is a gapful number since it is divisible by the number (48) 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 420735264768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (791142992640).

420735264768 is an abundant number, since it is smaller than the sum of its proper divisors (1161550720512).

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

420735264768 is a wasteful number, since it uses less digits than its factorization.

420735264768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 694 (or 665 counting only the distinct ones).

The product of its (nonzero) digits is 13547520, while the sum is 54.

The spelling of 420735264768 in words is "four hundred twenty billion, seven hundred thirty-five million, two hundred sixty-four thousand, seven hundred sixty-eight".