Prime Factorization Questions and Answers

1. Prime Factorization

Prime Factorization is a way of expressing a number as a multiplication of its prime factors. A prime number is a number which has only two factors, 1 and the number itself. 2, 3, 5, 7, 11, 13, 17, 19 and so on are examples of prime numbers. 

For example, to find the Prime factorization of 42:

We know that 42 = 6 x 7, but 6 is not a prime number. The number 6 can be further factored as 6 = 2 x 3, here 2 and 3 are prime numbers. So, we get the prime factorization of 42 = 2 x 3 x 7, where 2, 3 and 7 are prime numbers.

1.1 What are Factors and Prime Factors?

Factors are the numbers that can divide another number without any remainder. In other words, Factors of a number are the numbers that are multiplied to get the original number.

For example, finding the factors of 24:

All the numbers that are involved in these multiplications are the factors of the given number. Thus, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

However, Prime Factors of a number are the prime numbers that are multiplied to get the original number. Prime factors cannot be further split into more factors. For the same example, the prime factors of 24 are 2, 2, 2 and 3 i.e., 24 = 2 x 2 x 2 x 3.

Hence, Prime Factorization is kind of similar to factoring a number but it only considers prime numbers as the factors. 

1.2 Divisibility Rules

Divisibility rules are helpful in finding the prime factors of a number.

1.3 Methods of Prime Factorization

We can use the following methods:

• Prime factorization using factor tree method
• Prime factorization using division method

1.3.1 Prime factorization using factor tree method

Prime factorization using factor tree method can be done using the following steps:

• Consider the given number as the root of the factor tree.
• Write down the pair of factors which are the branches of the factor tree.
• Again factorise the composite factors, and write down the factor pairs as the branches.
• Repeat the step, until you find the prime factors of all the composite factors.
• Circle the prime factors obtained.
• Finally, write the prime factors in order by inserting a multiplication symbol between them.

For example, Prime Factorization of 750:

1.3.2 Prime factorization using division method

Prime factorization using division method can be done using the following steps:

• Divide the given number by the smallest prime number. This prime number should divide the number exactly.
• Again, divide the quotient obtained by the smallest prime number.
• Repeat the process, until the quotient itself becomes 1.
• Finally, insert a multiplication symbol between all the prime factors.

For example, Prime Factorization of 96: