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Prime Factorization

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Prime Factorization

Algebra-1

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You will write out a composite number as the product of its prime factors.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Determine the prime factorization of a composite number.

Everything You'll Have Covered

Characteristics of prime and composite numbers

A prime number is a whole number with exactly two positive divisors, itself and one.

For example,

2, 3, 5, 7, 11, 13, 17, 19, etc. are all prime numbers.

A composite number is a whole number that has factors other than 1 and itself.

For example,

4, 6, 9, 15, 32, 45, etc. are all composite numbers.

The number 0 has an infinite number of divisors (any nonzero whole number divides 0), but cannot be divided by itself (0/0 = undefined ) so it is not considered prime (prime numbers have exactly two divisors, 1 and itself). It cannot be written as a product of two factors, neither of which is itself, so 0 is not composite.

The number 1 has only one positive divisor, so it is not considered prime (prime numbers have exactly two divisors). It cannot be written as a product of two factors, neither of which is itself, so 1 is also not composite.

Using a factor tree starting with the least prime factor of the number

One method used to write out a number's prime factorization is to find two factors of the number, one of which is the least prime factor of the number.

For example,

Using a factor tree starting with two composite numbers

If the same number is written as a product of two composite numbers, its prime factorization does not change.

For example,

Dividing by prime numbers

Another method is to divide the number by its prime factors. In this method, the number is repeatedly divided by prime numbers, starting with its least prime factor until we get a prime number. Then all the prime divisors are written as prime factors of the number.

For example,

Dividing by Prime Numbers

Finding the least prime factors

This method is similar to building a factor tree with the least prime factor of the number, but without the factor tree. Start by finding the least prime factor of the number.

For example,

36 = 2 18 The least prime factor of 36 is 2.

Next find the least prime factor of 18.

= 2 2 9 The least prime factor of 18 is 2 (write 18 as 2 9).

= 2 2 3 3 The least prime factor of 9 is 3 (write 9 as 3 3).

Once we have all of the prime factors, we can write the prime factorization of the number using exponents.

36 = 2 3

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Learners should be familiar with divisibility, exponents, factors, prime numbers, and composite numbers.
Course Algebra-1
Type of Tutorial Procedural Development
Key Vocabulary composite numbers, factor, factor tree