Algebra Demystified 2nd Ed

Appendix FACTORING WITH PRIME NUMBERS 471

DeMYSTiFieD / Algebra DeMYSTiFieD / Gibilisco / 000-0 / Appendix

SOLUTIONS

1. 166: The prime numbers to check are 2, 7, 11.


2. 401: The prime numbers to check are 7, 11, 13, 17, 19.


3. 84: The prime numbers to check are 2, 3, 7.


4. 136: The prime numbers to check are 2, 7, 11.


5. 465: The prime numbers to check are 3, 5, 7, 11, 13, 17, 19.

To factor a number into its prime factors, we keep dividing the number by
the prime numbers in the list. A prime number might divide a number more
than once. For instance, 2 divides 12 twice; 12 = 2 ∙ 2 ∙ 3.

EXAMPLE

Factor 1224.

The prime factors to check are 2, 3, 7, 11, 13, 17, 19, 23, 29, 31.

1224 ÷ 2 = 612

612 ÷ 2 = 306

306 ÷ 2 = 153

153 ÷ 3 = 51

51 ÷ 3 = 17

1224 = 2 · 2 · 2 · 3 · 3 · 17

Factor 300.

The prime factors to check are 2, 3, 5, 7, 11, 13, 17.

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

300 = 2 · 2 · 3 · 5 · 5

EXAMPLE

Factor 1224.