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42672 = 2437127
BaseRepresentation
bin1010011010110000
32011112110
422122300
52331142
6525320
7235260
oct123260
964473
1042672
112a073
1220840
1316566
14117a0
15c99c
hexa6b0

42672 has 40 divisors (see below), whose sum is σ = 126976. Its totient is φ = 12096.

The previous prime is 42667. The next prime is 42677. The reversal of 42672 is 27624.

It is a happy number.

42672 is nontrivially palindromic in base 15.

It is an interprime number because it is at equal distance from previous prime (42667) and next prime (42677).

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 an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 42672.

It is not an unprimeable number, because it can be changed into a prime (42677) by changing a digit.

42672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 273 + ... + 399.

242672 is an apocalyptic number.

42672 is a gapful number since it is divisible by the number (42) 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 42672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (63488).

42672 is an abundant number, since it is smaller than the sum of its proper divisors (84304).

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

42672 is a wasteful number, since it uses less digits than its factorization.

42672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 145 (or 139 counting only the distinct ones).

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

The square root of 42672 is about 206.5720213388. The cubic root of 42672 is about 34.9446744962.

It can be divided in two parts, 42 and 672, that multiplied together give a square (28224 = 1682).

The spelling of 42672 in words is "forty-two thousand, six hundred seventy-two".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56 84 112 127 168 254 336 381 508 762 889 1016 1524 1778 2032 2667 3048 3556 5334 6096 7112 10668 14224 21336 42672