138240 has 88 divisors (see below), whose sum is σ = 491280. Its totient is φ = 36864.

The previous prime is 138239. The next prime is 138241. The reversal of 138240 is 42831.

It can be divided in two parts, 138 and 240, that added together give a triangular number (378 = T_{27}).

It is a happy number.

It is a Jordan-Polya number, since it can be written as 6! ⋅ 4! ⋅ (2!)^{3}.

It is an interprime number because it is at equal distance from previous prime (138239) and next prime (138241).

It is a super-2 number, since 2×138240^{2} = 38220595200, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138241) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 27646 + ... + 27650.

138240 is a Friedman number, since it can be written as 10*(8+2^4)^3, using all its digits and the basic arithmetic operations.

2^{138240} is an apocalyptic number.

138240 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 138240, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (245640).

138240 is an abundant number, since it is smaller than the sum of its proper divisors (353040).

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

138240 is an equidigital number, since it uses as much as digits as its factorization.

138240 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 138240 is about 371.8064012359. The cubic root of 138240 is about 51.7064325608.

The spelling of 138240 in words is "one hundred thirty-eight thousand, two hundred forty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 90 96 108 120 128 135 144 160 180 192 216 240 256 270 288 320 360 384 432 480 512 540 576 640 720 768 864 960 1024 1080 1152 1280 1440 1536 1728 1920 2160 2304 2560 2880 3072 3456 3840 4320 4608 5120 5760 6912 7680 8640 9216 11520 13824 15360 17280 23040 27648 34560 46080 69120 138240

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