How do you identify a prime number?  How do you decompose a number into a product of its prime factors?How do you find the LCM or HCF of two or more numbers?

Identifying a Prime Number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, and 13. To identify if a number is prime, you need to check if it has any divisors other than 1 and itself. If it does, it's not a prime number. If it doesn't, it is a prime number.

Decomposing a Number into a Product of its Prime Factors: This process is called prime factorization. To do this, start by dividing the number by the smallest prime number, which is 2. If the number is not divisible by 2, move on to the next prime number, which is 3, and so on. Continue this process until the number becomes 1. The prime numbers used to divide are the prime factors of the original number.

Finding the LCM (Least Common Multiple) and HCF (Highest Common Factor) of Two or More Numbers:

• LCM: The least common multiple of two numbers is the smallest number that is a multiple of both. To find the LCM, list the prime factors of each number, then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you only count it once in the LCM.

• HCF: The highest common factor of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF, list the prime factors of each number, then multiply those factors both numbers have in common. If a factor is common to both numbers, you only count it once in the HCF.