61416000 has 168 divisors, whose sum is σ = 219952824. Its totient is φ = 16358400.

The previous prime is 61415989. The next prime is 61416031. The reversal of 61416000 is 61416.

Added to its reverse (61416) it gives a triangular number (61477416 = T₁₁₀₈₈).

61416000 is a `hidden beast` number, since 61 + 4 + 1 + 600 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 13307904 + 48108096 = 3648^2 + 6936^2 .

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 23 ways as a sum of consecutive naturals, for example, 71574 + ... + 72426.

It is an arithmetic number, because the mean of its divisors is an integer number (1309243).

Almost surely, 2^61416000 is an apocalyptic number.

61416000 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 61416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109976412).

61416000 is an abundant number, since it is smaller than the sum of its proper divisors (158536824).

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

61416000 is a wasteful number, since it uses less digits than its factorization.

61416000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 886 (or 863 counting only the distinct ones).

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

The square root of 61416000 is about 7836.8360962827. The cubic root of 61416000 is about 394.5425457832.

Adding to 61416000 its reverse (61416), we get a palindrome (61477416).

61416000 divided by its reverse (61416) gives a cube (1000 = 10³).

The spelling of 61416000 in words is "sixty-one million, four hundred sixteen thousand".