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**465is an odd number**,as it is not divisible by 2

The factors for 465 are all the numbers between -465 and 465 , which divide 465 without leaving any remainder. Since 465 divided by -465 is an integer, -465 is a factor of 465 .

Since 465 divided by -465 is a whole number, -465 is a factor of 465

Since 465 divided by -155 is a whole number, -155 is a factor of 465

Since 465 divided by -93 is a whole number, -93 is a factor of 465

Since 465 divided by -31 is a whole number, -31 is a factor of 465

Since 465 divided by -15 is a whole number, -15 is a factor of 465

Since 465 divided by -5 is a whole number, -5 is a factor of 465

Since 465 divided by -3 is a whole number, -3 is a factor of 465

Since 465 divided by -1 is a whole number, -1 is a factor of 465

Since 465 divided by 1 is a whole number, 1 is a factor of 465

Since 465 divided by 3 is a whole number, 3 is a factor of 465

Since 465 divided by 5 is a whole number, 5 is a factor of 465

Since 465 divided by 15 is a whole number, 15 is a factor of 465

Since 465 divided by 31 is a whole number, 31 is a factor of 465

Since 465 divided by 93 is a whole number, 93 is a factor of 465

Since 465 divided by 155 is a whole number, 155 is a factor of 465

Multiples of 465 are all integers divisible by 465 , i.e. the remainder of the full division by 465 is zero. There are infinite multiples of 465. The smallest multiples of 465 are:

0 : in fact, 0 is divisible by any integer, so it is also a multiple of 465 since 0 × 465 = 0

465 : in fact, 465 is a multiple of itself, since 465 is divisible by 465 (it was 465 / 465 = 1, so the rest of this division is zero)

etc.

It is possible to determine using mathematical techniques whether an integer is prime or not.

for 465, the answer is:
**No, 465 is not a prime number**.

To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 465). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 21.564 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.

More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.

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