# why is 57 not a prime number

Mathematician: Note that when we say that a number is prime, all that we are doing is applying a definition that was devised by mathematicians. A prime number is generally defined to be any positive number that has exactly two distinct positive integer divisors (the divisors being 1 and the number itself). So 13 is prime, because it is divisible only by 1 and 13, whereas 14 is not prime because it is divisible by 1, 2, 7 and 14. Note that this excludes the number 1 from being prime. The biggest reason this definition of primality is used, as opposed to a slightly different one, is merely a matter of convenience. Mathematicians like to choose definitions in such a way that important theorems are simple and easy to state. Probably the most important theorem involving prime numbers is the Fundamental Theorem of Arithmetic, which says that all integers greater than 1 can be expressed as a

unique product of prime numbers up to reordering of the factors. So, for example, 54 can be written as which is a unique factorization assuming that we list the factors in decreasing order. Now, notice that if we counted 1 as a prime number, then this theorem would no longer hold as stated, since we would then be able to write so there would not be a single, unique representation for 54 as the theorem requires.

Hence, if we count 1 as a prime number, then the Fundamental Theorem ofArithmeticб would have to be restated as something like, all integers greater than 1 can be expressed as a unique product of prime numbers (not including 1) up to reordering of the factors. This is a tiny bit more cumbersome, but not horrible. If you have to work with prime numbers day in and day out though, simplifying theorems just a little bit (by choosing your definitions carefully) may well be worth it. Nonetheless, if mathematicians chose a slightly different definition for primality that included the number one, while they would then be forced to modify many of their theorems involving primes, the world wouldn t come crashing down on its head. Is 57 A Composite Number? Yes, number 57 is a composite number. Fifty-seven is a composite number, because it has more divisors than 1 and itself. Is 57 A Prime Number? No the number 57 is not a prime number. What Are The Prime Factors Of Fifty-seven?

The prime factors of number 57 are: 3, 19 So, if n > 0 is an integer and there are integers 1 < a, b < n such that n = a * b, then n is composite. By definition, every integer greater than one is either a prime number or a composite number. The number one is a unit, it is neither prime nor composite. For example, the integer 14 is a composite number because it can be factored as 2 * 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself. Every composite number can be written as the product of two or more (not necessarily distinct) primes, for example, the composite number 299 can be written as 13 * 23, and that the composite number 360 can be written as 23 * 32 * 5; furthermore, this representation is unique up to the order of the factors. This is called the fundamental theorem of arithmetic. About Number 5. Integers with a last digit as a zero or a five in the decimal system are divisible by five. Five is a prime number. All odd multiples of five border again with the five (all even with zero). The fifth number of the Fibonacci sequence is a five.

Five is also the smallest prime number that is the sum of all other primes which are smaller than themselves. The Five is a Fermat prime: 5 = 2 ^ {2 ^ 1} +1 and the smallest Wilson prime. Number five is a bell number (sequence A000110 in OEIS). There are exactly five platonic bodies. There are exactly five tetrominoes. About Number 7. Seven is a prime number. It is the lowest natural number that cannot be represented as the sum of the squares of three integers. The corresponding cyclic number is 142857. You can use this feature to calculate the result of the division of natural numbers by 7 without a calculator quickly. A seven-sided shape is a heptagon. One rule for divisibility by 7 leads to a simple algorithm to test the rest loose divisibility of a natural number by 7: Take away the last digit, double it and subtract them from the rest of the digits. If the difference is negative, then you're leaving the minus sign. If the result has more than one digit, so you repeat steps 1 through fourth. Eventually results are 7 or 0, then the number is divisible by 7 and not otherwise.

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