137424 has 40 divisors (see below), whose sum is σ = 406720. Its totient is φ = 39168.

The previous prime is 137413. The next prime is 137437. The reversal of 137424 is 424731.

137424 = T₃₂ + T₃₃ + ... + T₉₄.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a nude number because it is divisible by every one of its digits.

It is a self number, because there is not a number n which added to its sum of digits gives 137424.

It is a congruent number.

It is an unprimeable number.

137424 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 132 + ... + 540.

It is an arithmetic number, because the mean of its divisors is an integer number (10168).

2¹³⁷⁴²⁴ is an apocalyptic number.

137424 is a gapful number since it is divisible by the number (14) 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 137424, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (203360).

137424 is an abundant number, since it is smaller than the sum of its proper divisors (269296).

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

137424 is a wasteful number, since it uses less digits than its factorization.

137424 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 427 (or 421 counting only the distinct ones).

The product of its digits is 672, while the sum is 21.

The square root of 137424 is about 370.7074318111. The cubic root of 137424 is about 51.6044945307.

It can be divided in two parts, 137 and 424, that added together give a triangular number (561 = T₃₃).

The spelling of 137424 in words is "one hundred thirty-seven thousand, four hundred twenty-four".