61001is an odd number,as it is not divisible by 2
The factors for 61001 are all the numbers between -61001 and 61001 , which divide 61001 without leaving any remainder. Since 61001 divided by -61001 is an integer, -61001 is a factor of 61001 .
Since 61001 divided by -61001 is a whole number, -61001 is a factor of 61001
Since 61001 divided by -1 is a whole number, -1 is a factor of 61001
Since 61001 divided by 1 is a whole number, 1 is a factor of 61001
Multiples of 61001 are all integers divisible by 61001 , i.e. the remainder of the full division by 61001 is zero. There are infinite multiples of 61001. The smallest multiples of 61001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 61001 since 0 × 61001 = 0
61001 : in fact, 61001 is a multiple of itself, since 61001 is divisible by 61001 (it was 61001 / 61001 = 1, so the rest of this division is zero)
122002: in fact, 122002 = 61001 × 2
183003: in fact, 183003 = 61001 × 3
244004: in fact, 244004 = 61001 × 4
305005: in fact, 305005 = 61001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 61001, the answer is: yes, 61001 is a prime number because it only has two different divisors: 1 and itself (61001).
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 61001). 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 246.984 ). 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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