Expert: Josh - 1/24/2005

Question
Questions:
1. What is prime factor?
2. How do I figure out the greatest prime factors of 15, 14 respectively?

Thank you for your time.

Answer
Hi JJ,

(1) A factor is an integer which divides a larger integer, leaving us with no remainder.
So, assuming that "x" is less than "y", if "x" is a factor of "y", then "x" divides "y" perfectly. That is, we can express y as y=ax, where "y" is the dividend, "x" is the divisor and "a" represents the "quotient". Notice that there is no remainder here.

A "prime factor" is simply a factor that is also a prime number. By definition, a prime number contains no factor, other than 1 and the number itself. That is, a prime number cannot be further divided by any other number.

Consider the following example.

Let x=4, y=12.
Clearly, 4 divides 12, since 4*3=12.
So, 4 is a factor of 12.
Similarly, 2 divides 12, since 2*6=12.

However, 4 is NOT a prime factor of 12, because 4 can be further decomposed into a product. Very simply, 4=2*2, so it cannot be a prime number. On the other hand, 2 is a prime factor of 12.

(2)  Recall that a prime number is one which cannot be expressed as a product of two numbers other than 1 and the number itself.

Here, 15=3x5. Both 3 and 5 are prime factors of 15, because they divide 15 and they are both prime numbers.
5 is the larger of the two.

14=2x7. Both 2 and 7 turns out to be prime numbers. So, 7 is the greatest prime factor of 14.

Cheers.