61948800 has 240 divisors, whose sum is σ = 229561200. Its totient is φ = 16450560.

The previous prime is 61948787. The next prime is 61948801. The reversal of 61948800 is 884916.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (61948801) by changing a digit.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 259081 + ... + 259319.

It is an arithmetic number, because the mean of its divisors is an integer number (956505).

Almost surely, 2^61948800 is an apocalyptic number.

61948800 is a gapful number since it is divisible by the number (60) 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 61948800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114780600).

61948800 is an abundant number, since it is smaller than the sum of its proper divisors (167612400).

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

61948800 is a wasteful number, since it uses less digits than its factorization.

61948800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 275 (or 249 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The square root of 61948800 is about 7870.7559992672. The cubic root of 61948800 is about 395.6801825500.

The spelling of 61948800 in words is "sixty-one million, nine hundred forty-eight thousand, eight hundred".