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122400 = 25325217
BaseRepresentation
bin11101111000100000
320012220100
4131320200
512404100
62342400
71016565
oct357040
9205810
10122400
1183a63
125aa00
1343935
143286c
1526400
hex1de20

122400 has 108 divisors (see below), whose sum is σ = 457002. Its totient is φ = 30720.

The previous prime is 122399. The next prime is 122401. The reversal of 122400 is 4221.

It is an interprime number because it is at equal distance from previous prime (122399) and next prime (122401).

It can be written as a sum of positive squares in 3 ways, for example, as 104976 + 17424 = 324^2 + 132^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (122401) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 7192 + ... + 7208.

2122400 is an apocalyptic number.

122400 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 122400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (228501).

122400 is an abundant number, since it is smaller than the sum of its proper divisors (334602).

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

122400 is a wasteful number, since it uses less digits than its factorization.

122400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The square root of 122400 is about 349.8571136907. The cubic root of 122400 is about 49.6509016122.

Adding to 122400 its reverse (4221), we get a palindrome (126621).

The spelling of 122400 in words is "one hundred twenty-two thousand, four hundred", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 17 18 20 24 25 30 32 34 36 40 45 48 50 51 60 68 72 75 80 85 90 96 100 102 120 136 144 150 153 160 170 180 200 204 225 240 255 272 288 300 306 340 360 400 408 425 450 480 510 544 600 612 680 720 765 800 816 850 900 1020 1200 1224 1275 1360 1440 1530 1632 1700 1800 2040 2400 2448 2550 2720 3060 3400 3600 3825 4080 4896 5100 6120 6800 7200 7650 8160 10200 12240 13600 15300 20400 24480 30600 40800 61200 122400