It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 3 977 is not a prime number.
For example, 3 977 can be divided by 41: 3 977 / 41 = 97.
For 3 977 to be a prime number, it would have been required that 3 977 has only two divisors, i.e., itself and 1.
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3 977 is an odd number, because it is not evenly divisible by 2.
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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 3 977 is about 63.063.
Thus, the square root of 3 977 is not an integer, and therefore 3 977 is not a square number.
The square of a number (here 3 977) is the result of the product of this number (3 977) by itself (i.e., 3 977 × 3 977); the square of 3 977 is sometimes called "raising 3 977 to the power 2", or "3 977 squared".
The square of 3 977 is 15 816 529 because 3 977 × 3 977 = 3 9772 = 15 816 529.
As a consequence, 3 977 is the square root of 15 816 529.
The multiples of 3 977 are all integers evenly divisible by 3 977, that is all numbers such that the remainder of the division by 3 977 is zero. There are infinitely many multiples of 3 977. The smallest multiples of 3 977 are: