429012000 has 288 divisors, whose sum is σ = 1614425904. Its totient is φ = 107520000.

The previous prime is 429011959. The next prime is 429012011. The reversal of 429012000 is 210924.

It can be written as a sum of positive squares in 8 ways, for example, as 109746576 + 319265424 = 10476^2 + 17868^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×429012000² = 368102592288000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 611650 + ... + 612350.

Almost surely, 2^429012000 is an apocalyptic number.

429012000 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 429012000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (807212952).

429012000 is an abundant number, since it is smaller than the sum of its proper divisors (1185413904).

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

429012000 is a wasteful number, since it uses less digits than its factorization.

429012000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 749 (or 728 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 429012000 is about 20712.6048579120. The cubic root of 429012000 is about 754.2057053073.

Adding to 429012000 its reverse (210924), we get a palindrome (429222924).

It can be divided in two parts, 4290 and 12000, that added together give a triangular number (16290 = T₁₈₀).

The spelling of 429012000 in words is "four hundred twenty-nine million, twelve thousand".