Dr. Mark. A. Boster received his doctorate in Educational Leadership from Liberty University and conducted his research in gender roles in award-winning children’s books. He has over 24 years of experience in education at Columbus City Schools holding roles such as curriculum coordinator and classroom teacher.
In art class, Mrs. Thatcher wanted the students to draw trees. Some trees looked like clouds with a trunk, but Shantea wanted to draw a tree in the winter. She drew the trunk and then added straight lines connected to each other to look like branches.
Later that day, in math, the students learned to factor numbers. 'Hey,' Shantea said, 'It looks like my tree with Mrs. Thatcher!' And they did!
A prime number is a whole number larger than 1 that can only be divided by 1 and itself. An example of this would be the number 7. You can't divide anything into 7, except 7 and 1.
A factor is any number you can multiply by another number to get a third number. In the equation 4 x 5 = 20, both 4 and 5 are factors of 20.
Bet you can guess what is coming next. A prime factor is a factor that is also a prime number. All whole numbers can be factored into prime numbers.
These are all the prime factors under 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Factoring Numbers on a Tree
How about using some trees? Well, they sort of look like little number trees.
Let's see how to factor a number. How about the number 20? The factors of 20 can be 4 and 5 (since 4 x 5 = 20), or 2 and 10 (because 2 x 10 = 20). Let's use the 4 and 5 for now. Let's get that down to prime factors.
Can you divide anything into 4 or 5 other than 1 and the number itself? Well, not the 5, so 5 is one of the numbers we're looking for.
The 4 you can factor further because 2 x 2 = 4.
Can you divide anything into 2 other than 1 and 2? Nope, so you have two 2's as prime factors. Since there are two of them we can give 2 the exponent of 2. Let's take a moment to look at the 'Prime Factors of 20' diagram; this will show you the factor tree.
Now that you have the prime factors of 20, how about a larger number? Just do the same thing. Don't let a larger number scare you. Let's try 81. Well 9 x 9 = 81. Now ask yourself if anything can be divided into 9 other than 1 or 9.
Think to yourself to find what the factors are.
Does 2 times anything give me 9? Nope.
Does 3 times anything give me 9? Yes! 3 x 3 = 9. So, you can use 3s.
3 x 3 = 9 and 3 x 3 = the other 9. Hmm, can any number be multiplied together to get 3? Nope, just 1 and 3. So 3 must be a prime number! We have four 3s, so you can write an exponent of 4 (34).
Look at the 'Factors of 81' diagram if you need to.
A prime number is a whole number larger than 1 that can only be divided by 1 and itself. Furthermore, a factor is any number you can multiply by another number to get a third number. If you put those together you get a prime factor, which is a factor that is also a prime number.
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