137is an odd number,as it is not divisible by 2
The factors for 137 are all the numbers between -137 and 137 , which divide 137 without leaving any remainder. Since 137 divided by -137 is an integer, -137 is a factor of 137 .
Since 137 divided by -137 is a whole number, -137 is a factor of 137
Since 137 divided by -1 is a whole number, -1 is a factor of 137
Since 137 divided by 1 is a whole number, 1 is a factor of 137
Multiples of 137 are all integers divisible by 137 , i.e. the remainder of the full division by 137 is zero. There are infinite multiples of 137. The smallest multiples of 137 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 137 since 0 × 137 = 0
137 : in fact, 137 is a multiple of itself, since 137 is divisible by 137 (it was 137 / 137 = 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 137, the answer is: yes, 137 is a prime number because it only has two different divisors: 1 and itself (137).
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 137). 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 11.705 ). 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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