10077069313600 has 189 divisors, whose sum is σ = 25228433987913. Its totient is φ = 3961701120000.

The previous prime is 10077069313589. The next prime is 10077069313607. The reversal of 10077069313600 is 631396077001.

The square root of 10077069313600 is 3174440.

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

It can be written as a sum of positive squares in 13 ways, for example, as 5827666371136 + 4249402942464 = 2414056^2 + 2061408^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (10077069313607) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 7745632950 + ... + 7745634250.

Almost surely, 2^{10077069313600} is an apocalyptic number.

10077069313600 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10077069313600 is the 3174440-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10077069313600

10077069313600 is an abundant number, since it is smaller than the sum of its proper divisors (15151364674313).

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

10077069313600 is an frugal number, since it uses more digits than its factorization.

10077069313600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2746 (or 1369 counting only the distinct ones).

The product of its (nonzero) digits is 142884, while the sum is 43.

The spelling of 10077069313600 in words is "ten trillion, seventy-seven billion, sixty-nine million, three hundred thirteen thousand, six hundred".