127264000 has 144 divisors (see below), whose sum is σ = 328111056. Its totient is φ = 49152000.

The previous prime is 127263973. The next prime is 127264001. The reversal of 127264000 is 462721.

It can be written as a sum of positive squares in 8 ways, for example, as 79709184 + 47554816 = 8928^2 + 6896^2 .

It is a super-2 number, since 2×127264000² = 32392251392000000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (127264001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1311952 + ... + 1312048.

It is an arithmetic number, because the mean of its divisors is an integer number (2278549).

Almost surely, 2^127264000 is an apocalyptic number.

127264000 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 127264000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (164055528).

127264000 is an abundant number, since it is smaller than the sum of its proper divisors (200847056).

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

127264000 is an frugal number, since it uses more digits than its factorization.

127264000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 169 (or 145 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 22.

The square root of 127264000 is about 11281.1346947016. The cubic root of 127264000 is about 503.0006231655. Note that the first 3 decimals are identical.

The spelling of 127264000 in words is "one hundred twenty-seven million, two hundred sixty-four thousand".