Fundamentals of Math

Fundamentals of Mathematics

Factors Factoring is like taking a number apart - the number becomes expressed as a product of its elements. The values that make up the product are either prime or composite.

Primes

Prime numbers are whole numbers that cannot be made by multiplying other whole numbers. Alternatively, a number whose only factors are 1 and itself.

Composites

Composite numbers are whole numbers that can be made by multiplying other whole numbers. Alternatively, a number which can be decomposed into factors other than 1 and itself. We ultimately strive to write a composite number as a product of all prime numbers. This product list is known as prime factorization .

Example 1.3.1

Find the prime factorization of 135.

1. 27 times 5 equals to 135, 5 is prime, but 27 is composite, so we can keep going.

2. 9 times 3 equals to 27, 3 is prime, but 9 is composite, so we can keep going.

3. 3 times 3 equals to 9, 3 is prime and there are no other composite numbers to factor, so we are finished.

The prime factorization of 135 is …

135 = 3 × 3 × 3 × 5

Returning to our original discussion of factors - factors can be prime or composite. Some questions may specifically ask you to decompose a number into a product of exclusively prime numbers (prime factorization). In this instance, the quickest method is to create a factor tree (see example 1.3.1); or they may state you should list all possible factors of a number. To list all the factors of a number, start with 1 and then place the number at opposite end.

Example 1.3.2

List all the factors of 42.

1 __________________________________________________42

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