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.
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.
- "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.
- 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.
- 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.
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.
- 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 .
- 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.
- 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.
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.
- 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.
- 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 .
- 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