# Is the number 1 prime composite or neither?

A

**natural**number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it has exactly two positive**factors**, 1 and the number itself.**Natural**numbers that have more than two positive**factors**are called composite. 1 has only one positive**factor**i.e. no.1 only. Hence 1 is neither prime nor composite.A.

### What is the smallest prime number and why?

1 is the

**smallest**natural**number**but it has only 1**factor**that is 1 itself. Therefore, 1 cannot be considered as a**prime number**. Next**number**2 is the**smallest**even**prime number**. as 1×1=1,so it is not**prime no**.#### Why number 1 is not a prime number?

"A**prime number**(or a**prime**) is a natural**number**greater than**1**that has no positive divisors other than**1**and itself. "**1**could be divided by**1**and itself. Therefore, if**1**is**prime**, it does**not**allow for any composite positive integer to be written as a unique product of primes.#### Is the number 57 a prime number?

**57**has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree. Although**57**is not**prime**, it is jokingly known as the "Grothendieck**prime**" after a story in which mathematician Alexander Grothendieck supposedly gave it as an example of a particular**prime number**.**57**is a 20-gonal**number**.#### Is the number 93 prime or composite?

Because 79 is less than 100 and isn't divisible by 2, 3, 5, or 7, you know that 79 is a**prime number**. Now test whether**93**is**prime**or composite:**93**is an odd**number**, so it isn't divisible by 2.**93**has a digital root of 3 (because 9 + 3 = 12 and 1 + 2 = 3), so**93**is divisible by 3.

B.

### Why is the number 1 not a prime number?

Answer

**One**: By definition of**prime**! An integer greater than**one**is called a**prime number**if its only positive divisors (factors) are**one**and itself.#### Is the number 1 an odd number?

An**odd number**is an integer of the form , where is an integer. The**odd numbers**are therefore , , ,**1**, 3, 5, 7, Integers which are not**odd**are called even.**Odd numbers**leave a remainder of**1**when divided by two, i.e., the congruence holds for**odd**.#### Is the number 123 a prime number?

To be**123 a prime number**, it would have been required that**123**has only two divisors, i.e., itself and 1. However,**123**is a semiprime (also called biprime or 2-almost-**prime**), because it is the product of a two non-necessarily distinct**prime numbers**. Indeed,**123**= 3 x 41, where 3 and 41 are both**prime numbers**.#### Is the number 21 a prime number?

**21**is a composite**number**. No**21**is not a**prime number**because a**prime number**is defined as a**number**which has 1 and the**number**itself as facors.**21**has 1, 3, 7 and**21**as factors so**21**is not a**prime number**.

C.

### What is the lowest composite number?

A composite number is a positive integer which is not prime (i.e., which has

**factors**other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16, (OEIS A002808), whose prime decompositions are summarized in the following table.#### Why is 1 not prime or composite?

A natural number (i.e.**1**, 2, 3, 4, 5, 6, etc.) is called a**prime**number (or a**prime**) if it has exactly two positive factors,**1**and the number itself. Natural numbers that have more than two positive factors are called**composite**.**1**has only**one**positive factor i.e. no.**1**only. Hence**1**is**neither prime nor composite**.#### What is the smallest even number?

So 0 is the**smallest**positive**even number**. In Mathematics, an**even number**is defined as an Integer which can be expressed in the form of 2k, where 'k' is any non-negative integer. The**number**0 easily holds the property to be the non-negative integer k. Thus we get an**even number**x .#### What is the largest prime number that is less than 100?

There are 25**prime numbers less than 100**. They are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, and 97.

Updated: 3rd October 2019