How is finding the factors of a number different from finding the prime factorization of a number?
Finding factors of a number is different from finding the prime factorization.
Answer: Prime factorization of a number is expressing the number as a product of its prime factors. Further factorizing a number is to write the number as the product of its factors.
Let's see in detail.
Factors of a number are the numbers that divide the given number without leaving any remainder.
Prime factorization of a number is the process of writing all the prime factors of that number that can be multiplied to get back the given number.
Let's find the factors and prime factorization of 12.
Factors of 12 can be found in many ways:
12 = 1 × 12, which contains factors 1, and 12 (composite).
or 12 = 2 × 6, which contains factors 2 (prime), and 6 (composite)
or 12 = 3 × 4, which contains factors 3 (prime), and 4 (composite)
The above three calculations are the factorization of the number 12.
or 12 = 2 × 2 × 3, which contains factors 2 (prime), and 3 (prime)
Here in this above calculation, we have performed the prime factorization of 12.
Hence, Factors of 12 = 1, 2, 3, 4, 6, 12, which contains 1, primes(2, 3) and composites(4, 6, 12)
Prime factorization of 12 = 2 × 2 × 3, which is unique.
Thus, finding the factors is different from the prime factorization.