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121968 = 24327112
BaseRepresentation
bin11101110001110000
320012022100
4131301300
512400333
62340400
71015410
oct356160
9205270
10121968
1183700
125a700
1343692
1432640
1526213
hex1dc70

121968 has 90 divisors (see below), whose sum is σ = 428792. Its totient is φ = 31680.

The previous prime is 121967. The next prime is 121993. The reversal of 121968 is 869121.

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

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (121963) 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, 11083 + ... + 11093.

2121968 is an apocalyptic number.

121968 is a gapful number since it is divisible by the number (18) 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 121968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (214396).

121968 is an abundant number, since it is smaller than the sum of its proper divisors (306824).

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

121968 is a wasteful number, since it uses less digits than its factorization.

121968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 43 (or 23 counting only the distinct ones).

The product of its digits is 864, while the sum is 27.

The square root of 121968 is about 349.2391730605. The cubic root of 121968 is about 49.5924199308.

Subtracting from 121968 its product of digits (864), we obtain a square (121104 = 3482).

It can be divided in two parts, 121 and 968, that added together give a square (1089 = 332).

The spelling of 121968 in words is "one hundred twenty-one thousand, nine hundred sixty-eight".

Divisors: 1 2 3 4 6 7 8 9 11 12 14 16 18 21 22 24 28 33 36 42 44 48 56 63 66 72 77 84 88 99 112 121 126 132 144 154 168 176 198 231 242 252 264 308 336 363 396 462 484 504 528 616 693 726 792 847 924 968 1008 1089 1232 1386 1452 1584 1694 1848 1936 2178 2541 2772 2904 3388 3696 4356 5082 5544 5808 6776 7623 8712 10164 11088 13552 15246 17424 20328 30492 40656 60984 121968