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103968 = 2532192
BaseRepresentation
bin11001011000100000
312021121200
4121120200
511311333
62121200
7612054
oct313040
9167550
10103968
1171127
1250200
1338427
1429c64
1520c13
hex19620

103968 has 54 divisors (see below), whose sum is σ = 312039. Its totient is φ = 32832.

The previous prime is 103967. The next prime is 103969. The reversal of 103968 is 869301.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is an interprime number because it is at equal distance from previous prime (103967) and next prime (103969).

It can be written as a sum of positive squares in only one way, i.e., 51984 + 51984 = 228^2 + 228^2 .

It is an ABA number since it can be written as A⋅BA, here for A=2, B=228.

It is not an unprimeable number, because it can be changed into a prime (103963) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 5463 + ... + 5481.

103968 is a Friedman number, since it can be written as 1083*96, using all its digits and the basic arithmetic operations.

2103968 is an apocalyptic number.

103968 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 103968

103968 is an abundant number, since it is smaller than the sum of its proper divisors (208071).

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

103968 is a wasteful number, since it uses less digits than its factorization.

103968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 54 (or 24 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 103968 is about 322.4406922211. The cubic root of 103968 is about 47.0218700090.

It can be divided in two parts, 10396 and 8, that added together give a square (10404 = 1022).

The spelling of 103968 in words is "one hundred three thousand, nine hundred sixty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 19 24 32 36 38 48 57 72 76 96 114 144 152 171 228 288 304 342 361 456 608 684 722 912 1083 1368 1444 1824 2166 2736 2888 3249 4332 5472 5776 6498 8664 11552 12996 17328 25992 34656 51984 103968