# Video: The Highest Common Factor

Find the greatest common factor of 63 and 42.

02:28

### Video Transcript

Find the greatest common factor of 63 and 42.

Before we can find the greatest common factor of 63 and 42, we just need to find the factors of 63 and 42. Let’s do this by creating a factor tree.

Factors of 63 are of course one and 63. Also I recognize that 63 is divisible by three. Three times 21 equals 63. 21 is also divisible by three. Three times seven equals 21.

Let’s do the same thing with 42. One times 42 equals 42. Two times 21 equals 42. 21 is divisible by three. Three times seven equals 21.

Now what we’re going to do is we’re going to write out all the prime factors of 63 and 42. 63 equals one times three times three times seven. 42 equal one times two times three times seven.

The next thing that we’re going to do is we’re going to circle all the shared prime factors, all the prime factors that are found on both lists. Both 42 and 63 have a prime factor of three. Both 63 and 42 have a prime factor of seven. Three times seven is 21, and that makes 21 the greatest common factor of 63 and 42.

Using prime factorization, we found all the common prime factors, multiplied those together to give us the greatest common factor of 63 and 42; it’s 21.