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.
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.
- Zero is an even number. As a result, zero shares all the properties that characterize even numbers: 0 is divisible by 2, 0 is neighbored on both sides by odd numbers, 0 is the sum of an integer (0) with itself, and a set of 0 objects can be split into two equal sets.
- The current definition of a prime number is a positive integer greater than 1 (i.e. the counting numbers 2, 3, 4, 5, etc.) whose only divisors are 1 and itself. A composite number is a positive integer greater than 1 which is not prime. Zero is not positive, so it falls outside the prime/composite categorization.
- 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.
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 factor of a multiple and the greatest factor of a multiple is the multiple itself. Property (4): Every number other than 1 has at least two factors, namely the number itself and 1.
- Why some people say it's not prime: It doesn't have exactly two positive divisors. The statement "1 is prime" is false false . Proof: The definition of a prime number is a positive integer that has exactly two positive divisors. However, 1 only has one positive divisor (1 itself), so it is not prime.
- A composite number is a number that can be divided evenly by more numbers than 1 and itself. It is the opposite of a prime number. The number 81 can be evenly divided by 1, 3, 9, 27 and 81, with no remainder. Since 81 cannot be divided by just 1 and 81, it is a 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.
- 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 .
- A factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number. Example: The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers). See: Prime Number. Prime Factorization.
- Summary: A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite. The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 since each of these numbers has only two factors, itself and 1.
Updated: 29th September 2018