7648000 has 72 divisors (see below), whose sum is σ = 19131840. Its totient is φ = 3046400.

The previous prime is 7647989. The next prime is 7648001. The reversal of 7648000 is 8467.

7648000 = T₁₀₅ + T₁₀₆ + ... + T₃₆₀.

7648000 is nontrivially palindromic in base 15.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7648001) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 31881 + ... + 32119.

It is an arithmetic number, because the mean of its divisors is an integer number (265720).

Almost surely, 2^7648000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9565920).

7648000 is an abundant number, since it is smaller than the sum of its proper divisors (11483840).

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

7648000 is an equidigital number, since it uses as much as digits as its factorization.

7648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 270 (or 246 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 25.

The square root of 7648000 is about 2765.5017627910. The cubic root of 7648000 is about 197.0225609109.

The spelling of 7648000 in words is "seven million, six hundred forty-eight thousand".