Final answer:
The number between eight and thirteen with the prime factors of two and three is 12, as it is the multiple of 6 (2×3) within the given range. The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1.
Step-by-step explanation:
The question asks to find a number that is between eight and thirteen, and which has two and three as its prime factors. To find a number within this range that has both 2 and 3 as prime factors, we need to find their least common multiple within the given range. Since 2 and 3 are prime, any number that is their product will have both as factors. Therefore, we multiply 2 and 3 together to find the number, which is 2 × 3 = 6.
However, since 6 is not between eight and thirteen, we consider the smallest multiple of 6 that falls within the range. Multiplying 6 by 2 gives us 12, which is between eight and thirteen and has both 2 and 3 as prime factors.
Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers. Here, all the concepts of prime factors and prime factorization methods have been explained which will help the students understand how to find the prime factors of a number easily.
The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorized. Therefore, 30 = 2 x 3 x 5, where 2,3 and 5 are prime factors.
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and so on. These prime numbers when multiplied with any natural numbers produce composite numbers.