# Even, Odd, Prime and Composite Numbers

**Even and Odd**: Any integer which is divisible by two is called an even number. Any integer which is not divisible by two is called an odd number.

**N.B.:** Zero has not been categorized in either of the two categories.

**Prime and Composite** : Any integer which is divisible by 1 and itself only is called a prime number. All integers which are not prime are called composite number as they are composed of two or more prime numbers.

**N.B.:** 1 is not a prime number.

**Positive and negative**: Any number which is greater than 0 is positive. Any number less than that is negative.

**Perfect numbers**:- If the sum of the divisors of N, excluding N itself, is equal to N, then N is called a perfect number. e.g. 6, 28, 496, 8128 etc.

6 = 1 + 2 + 3;

28 = 1 + 2 + 4 + 7 + 14;

496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248.

Keep posting stuff like this i really like it

@K.T. now this is very simple. To find out the total number of factors of a composite we break it into it’s prime factors. The number of factors depends on the number of times the prime same prime factor occurs in a number. If we consider 1 as a prime number, we cann’t restrict the number of time 1 can come. Again, it’s mathematics dear, we cann’t say why are you taking 1 again and again. If the product is not changing one can take one as many times as he wants. Which will distort the outcome of number of factors of a composite number. Similarly results of various mathematical operations will be distored.

Thank you for your attention and reply. But as you know and you daid it:

An important fact is that any number can be written as the product (multiplication) of prime numbers in one way

Wiyj all my respect to you, please allow me to say soamething different.

I agree with abovesaid definition, but you could not use 1 unlimited times when create product. What is the ground of this? You should use prime factors once only.

In your example 12=2*2*3, the number 2 is written twice because there are two factors of 2 (4=2*2), but nut multiple 1′s

Supose 1 is a prime, you will reach the result- 1(prine)*2(prime)*2(prime)*3(prime).

@K.T:

For others help I have posted your query and the explanation to it as a post. Here is the link

http://www.quickermaths.com/why-is-1-not-a-prime-number/

Hey K.T.

I greatly appreciate your interest in the subject and your logical doubt regarding 1 being not a prime number. I hope the given below explanation will be satisfy you-

No, not by the official definition, because it only has a single natural number divisor: 1. This is why the “exception” had to be made, that 1 is not a prime number.

In short: the definition as we know it is a simplification that doesn’t work completely – except if we specify that 1 is not included.

But why is it important for 1 not to be a prime number? It’s not just a matter of nitpicking. If 1 is not a prime number, then any composite number (such as 12) can be written as a product of primes in only one way (here, 2*2*3), not counting different orders. However, if 1 were a prime number, there would be infinitely many ways! We could write 12 for example, as 2*2*3, or 1*2*2*3, or 1*1*1*1*1*2*2*3. Having only one way to write a number as a product of primes is very useful when doing math.

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Prime and Composite : Any integer which is divisible by 1 and itself only is called a prime number.

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N.B.: 1 is not a prime number.

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Could you explaine what is the creteria thar excludes 1 from the list of prime numbers?

a) 1 is integer

b) 1 is divisible by 1 and itself (1)

Since anybody in the past has declared that 1 is not prime number, why we should follow this without thinking and contravene the general rule for prime numbers?

Is 1 as a figure is something which has come from the thin air. It is and always will be an integer. The criteria for 2 are the same – divisible by 1 and itself. And for all prime numbers.

Most probably the 1 is “guilty” because with 1 starts the series on numbers (natural, odd or prime). Suppose 2 was the beginning of the series. Should we ignore 2, because series starts with 2?