7961284800 has 504 divisors, whose sum is σ = 33769066320. Its totient is φ = 1819238400.

The previous prime is 7961284777. The next prime is 7961284801. The reversal of 7961284800 is 84821697.

It is a tau number, because it is divible by the number of its divisors (504).

It is a super-2 number, since 2×7961284800² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (7961284801) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2114920 + ... + 2118680.

Almost surely, 2^7961284800 is an apocalyptic number.

7961284800 is a gapful number since it is divisible by the number (70) 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 7961284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16884533160).

7961284800 is an abundant number, since it is smaller than the sum of its proper divisors (25807781520).

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

7961284800 is a wasteful number, since it uses less digits than its factorization.

7961284800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3806 (or 3778 counting only the distinct ones).

The product of its (nonzero) digits is 193536, while the sum is 45.

The square root of 7961284800 is about 89226.0320758466. The cubic root of 7961284800 is about 1996.7685148974.

The spelling of 7961284800 in words is "seven billion, nine hundred sixty-one million, two hundred eighty-four thousand, eight hundred".