701is an odd number,as it is not divisible by 2
The factors for 701 are all the numbers between -701 and 701 , which divide 701 without leaving any remainder. Since 701 divided by -701 is an integer, -701 is a factor of 701 .
Since 701 divided by -701 is a whole number, -701 is a factor of 701
Since 701 divided by -1 is a whole number, -1 is a factor of 701
Since 701 divided by 1 is a whole number, 1 is a factor of 701
Multiples of 701 are all integers divisible by 701 , i.e. the remainder of the full division by 701 is zero. There are infinite multiples of 701. The smallest multiples of 701 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 701 since 0 × 701 = 0
701 : in fact, 701 is a multiple of itself, since 701 is divisible by 701 (it was 701 / 701 = 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 701, the answer is: yes, 701 is a prime number because it only has two different divisors: 1 and itself (701).
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 701). 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 26.476 ). 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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