Explain what a prime number is. Before someone can learn how to do prime factorization, she must understand what it means and what a prime number is.
Choose a number that is a prime number. For example, to factor the number 17, determine if there are any numbers that 17 is divisible by. Because there are none, the prime factorization of 17 is 1 x 17.
Teach prime factorization by starting small. For example, determine what the prime factorization of 6 is. To do this, look at what numbers divide into six. Two multiplied by three is equal to six, and both of these numbers are prime numbers. Therefore, the prime factorization of 6 is 2 x 3.
Try more challenging examples. For example, find the prime factorization of 36. Divide 36 by several prime numbers to accomplish this. Dividing 36 by 2 equals 18. 18 divided by 2 equals 9 and 9 divided by three equals three. The prime factorization of 36 therefore is 2 x 2 x 3 x 3. Double-check the answer by multiplying these four numbers.
Choose a larger number. For example, try factoring the number 154. Because this is a relatively large number, find the prime factorization by dividing it by some prime numbers to see if any of them are factors of 154. Divide 154 by 2. This divides easily into a whole number of 77. At this point, you know that one prime number of 154 is 2. This leaves the factoring at 2 x 77. Determine if 77 is a prime number by dividing other prime numbers into it. It is not an even number, so it cannot be divided again by 2. Try dividing it by 3, 5 or 7, which are all prime numbers. The only one that works is 7. Seventy-seven divided by 7 equals 11. Therefore, the prime factorization of 154 is 2 x 7 x 11. Double-check the answer by multiplying these three prime numbers.