43is an odd number,as it is not divisible by 2
The factors for 43 are all the numbers between -43 and 43 , which divide 43 without leaving any remainder. Since 43 divided by -43 is an integer, -43 is a factor of 43 .
Since 43 divided by -43 is a whole number, -43 is a factor of 43
Since 43 divided by -1 is a whole number, -1 is a factor of 43
Since 43 divided by 1 is a whole number, 1 is a factor of 43
Multiples of 43 are all integers divisible by 43 , i.e. the remainder of the full division by 43 is zero. There are infinite multiples of 43. The smallest multiples of 43 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 43 since 0 × 43 = 0
43 : in fact, 43 is a multiple of itself, since 43 is divisible by 43 (it was 43 / 43 = 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 43, the answer is: yes, 43 is a prime number because it only has two different divisors: 1 and itself (43).
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 43). 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 6.557 ). 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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