It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 101, the answer is: yes, 101 is a prime number because it has only two distinct divisors: 1 and itself (101).
As a consequence, 101 is only a multiple of 1 and 101..
Since 101 is a prime number, 101 is also a deficient number, that is to say 101 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 101 without 101 itself (that is 1, by definition!).
Parity of 101
101 is an odd number, because it is not evenly divisible by 2.
Is 101 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 101 is about 10.050.
Thus, the square root of 101 is not an integer, and therefore 101 is not a square number.
Anyway, 101 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 101?
The square of a number (here 101) is the result of the product of this number (101) by itself (i.e., 101 × 101); the square of 101 is sometimes called "raising 101 to the power 2", or "101 squared".
As a consequence, 101 is the square root of 10 201.
Number of digits of 101
101 is a number with 3 digits.
What are the multiples of 101?
The multiples of 101 are all integers evenly divisible by 101, that is all numbers such that the remainder of the division by 101 is zero. There are infinitely many multiples of 101. The smallest multiples of 101 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 101 too, since 0 × 101 = 0
- 101: indeed, 101 is a multiple of itself, since 101 is evenly divisible by 101 (we have 101 / 101 = 1, so the remainder of this division is indeed zero)
- 202: indeed, 202 = 101 × 2
- 303: indeed, 303 = 101 × 3
- 404: indeed, 404 = 101 × 4
- 505: indeed, 505 = 101 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 101). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 10.050). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.