772148838400 has 135 divisors (see below), whose sum is σ = 1916266357831. Its totient is φ = 308634583040.

The previous prime is 772148838367. The next prime is 772148838403. The reversal of 772148838400 is 4838841277.

The square root of 772148838400 is 878720.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 201048211456 + 571100626944 = 448384^2 + 755712^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (772148838403) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 562380114 + ... + 562381486.

Almost surely, 2^772148838400 is an apocalyptic number.

772148838400 is the 878720-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 772148838400

772148838400 is an abundant number, since it is smaller than the sum of its proper divisors (1144117519431).

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

772148838400 is an frugal number, since it uses more digits than its factorization.

772148838400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2784 (or 1380 counting only the distinct ones).

The product of its (nonzero) digits is 2408448, while the sum is 52.

It can be divided in two parts, 7721 and 48838400, that added together give a square (48846121 = 6989²).

The spelling of 772148838400 in words is "seven hundred seventy-two billion, one hundred forty-eight million, eight hundred thirty-eight thousand, four hundred".