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46464 = 273112
BaseRepresentation
bin1011010110000000
32100201220
423112000
52441324
6555040
7252315
oct132600
970656
1046464
1131a00
1222a80
13181c2
1412d0c
15db79
hexb580

46464 has 48 divisors (see below), whose sum is σ = 135660. Its totient is φ = 14080.

The previous prime is 46457. The next prime is 46471.

46464 is nontrivially palindromic in base 10.

It is an interprime number because it is at equal distance from previous prime (46457) and next prime (46471).

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (24).

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

46464 is an undulating number in base 10.

Its product of digits (2304) is a multiple of the sum of its prime divisors (16).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 4219 + ... + 4229.

246464 is an apocalyptic number.

46464 is a gapful number since it is divisible by the number (44) 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 46464, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (67830).

46464 is an abundant number, since it is smaller than the sum of its proper divisors (89196).

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

46464 is a wasteful number, since it uses less digits than its factorization.

46464 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 16 counting only the distinct ones).

The product of its digits is 2304, while the sum is 24.

The square root of 46464 is about 215.5550973649. Note that the first 3 decimals coincide. The cubic root of 46464 is about 35.9505493883.

Multiplying 46464 by its sum of digits (24), we get a square (1115136 = 10562).

46464 divided by its sum of digits (24) gives a square (1936 = 442).

It can be divided in two parts, 464 and 64, that added together give a triangular number (528 = T32).

The spelling of 46464 in words is "forty-six thousand, four hundred sixty-four".