137968600 has 288 divisors, whose sum is σ = 438543360. Its totient is φ = 39168000.

The previous prime is 137968591. The next prime is 137968637. The reversal of 137968600 is 6869731.

137968600 = T₄₈₄ + T₄₈₅ + ... + T₉₇₉.

137968600 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a zygodrome in base 13.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 4450585 + ... + 4450615.

It is an arithmetic number, because the mean of its divisors is an integer number (1522720).

Almost surely, 2^137968600 is an apocalyptic number.

137968600 is a gapful number since it is divisible by the number (10) 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 137968600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (219271680).

137968600 is an abundant number, since it is smaller than the sum of its proper divisors (300574760).

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

137968600 is a wasteful number, since it uses less digits than its factorization.

137968600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 99 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 54432, while the sum is 40.

The square root of 137968600 is about 11746.0035756848. The cubic root of 137968600 is about 516.7257280153.

The spelling of 137968600 in words is "one hundred thirty-seven million, nine hundred sixty-eight thousand, six hundred".