Question

How is finding the factors of a number different from finding the prime factorization of a number?

Answer 1

Answer:

Finding prime factorization makes it easy to find the numbers which when multiplied will give the original number.

Step-by-step explanation:

We know that,

Factors are the numbers which are multiplied to get the original number.

Prime Factorization is the process to find the prime numbers which are multiplied to get the original number.

For e.g. Let us consider the number 228.

Now, the factors of 228 are the number which divide 228 i.e. 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228.

Thus, multiplying these numbers will give us the result as 228.

Moreover, to make the task of finding the numbers which multiply together to give that number, we use prime factorization.

Now, the prime factors of 228 are the prime numbers which divide 228 i.e.  2, 2, 3, 19.

Thus, instead of multiplying the 12 numbers which were the factors of 228, we just need to multiply 4  numbers representing the prime factors of 228.

Hence, finding prime factorization makes it easy to find the numbers which when multiplied will give the original number.