7is an odd number,as it is not divisible by 2
The factors for 7 are all the numbers between -7 and 7 , which divide 7 without leaving any remainder. Since 7 divided by -7 is an integer, -7 is a factor of 7 .
Since 7 divided by -7 is a whole number, -7 is a factor of 7
Since 7 divided by -1 is a whole number, -1 is a factor of 7
Since 7 divided by 1 is a whole number, 1 is a factor of 7
Multiples of 7 are all integers divisible by 7 , i.e. the remainder of the full division by 7 is zero. There are infinite multiples of 7. The smallest multiples of 7 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 7 since 0 × 7 = 0
7 : in fact, 7 is a multiple of itself, since 7 is divisible by 7 (it was 7 / 7 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 7, the answer is: yes, 7 is a prime number because it only has two different divisors: 1 and itself (7).
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 7). 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 2.646 ). 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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