137768400 has 540 divisors, whose sum is σ = 615255264. Its totient is φ = 28224000.

The previous prime is 137768383. The next prime is 137768417. The reversal of 137768400 is 4867731.

It is an interprime number because it is at equal distance from previous prime (137768383) and next prime (137768417).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 1940365 + ... + 1940435.

Almost surely, 2^137768400 is an apocalyptic number.

137768400 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 137768400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (307627632).

137768400 is an abundant number, since it is smaller than the sum of its proper divisors (477486864).

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

137768400 is a wasteful number, since it uses less digits than its factorization.

137768400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The square root of 137768400 is about 11737.4784344850. The cubic root of 137768400 is about 516.4756745790.

The spelling of 137768400 in words is "one hundred thirty-seven million, seven hundred sixty-eight thousand, four hundred".