Composite Numbers

A composite number is any whole number that has at least 3 factors; it can be divided by more than just 1 and itself.

Examples of composite numbers include 4, 12, 999, and 50. A few rules to remember when trying to identify composite numbers:

• all even numbers, except for 2, are composite
• any number ending in 5 or 0, except for 5, are composite
• composite numbers have at least 3 factors

Prime factorization

2 × 2 × 3 × 3, which can also be written as 2² x 3² is called the prime factorization of 36.

One way to find the prime factorization of a number is by making a factor tree. This involves starting with any pair of factors for a number and then factoring those factors until you can’t do so anymore.

We can also find prime factors by division method.

The steps below demonstrates how to factor 70 using the division method.

Step 1: Begin with a list of all primes whose squares are less than the number to be factored.

2, 3, 5, 7

Step 2: Divide 70 by 2. The result is 35.

Step 3: 2 does not divide 35, so we are done with 2. Cross 2 off the list of primes. 3 does not divide 35, so cross out 3. 5 divides 35, and the result is 7.

Step 4: When the result is prime, you have completed the process. Since 7 is prime, we have complete the prime factorization of 70.

Therefore the prime factors of 70 are 2 x 5 x 7

Exercise

List all factors of the given number.

1. 219
2. 15
3. 35
4. 40
5. 80
6. 828
7. 120
8. 150
9. 2211
10. 250
11. 71
12. 15,500

Determine whether each number is prime or composite.

1. 69
2. 71
3. 89
4. 91
5. 111
6. 169
7. 223
8. 247
9. 111,111
10. 101,001
11. 221
12. 271

Find the prime factorization of each number. If the number is prime, write prime.

1. 20
2. 30
3. 42
4. 52
5. 60
6. 64
7. 140
8. 160
9. 210
10. 220
11. 242
12. 248
13. 231
14. 237
15. 249
16. 251
17. 264
18. 369
19. 484
20. 480
21. 495
22. 497
23. 377
24. 399
25. 351
26. 435