Numbers in their Prime

Factor-T

In a Factor-T, you will have two columns: the left column with the prime numbers and the right column with progressively smaller quotients from division. Step 1: Determine a prime number that divides into your given number. Write that number in the left column. Step 2: Write the quotient of your number divided by the prime number in the right hand column. example of factor-t Step 3: Now look for a prime number that divides into the quotient, 39 in this case. Continue steps 1 and 2 until you have a one in the right-hand column. The numbers on the left are your prime factorization! example of factor-t The prime factorization of 78 is 2 x 3 x 13. No other number has this prime factorization. Here is another example for the prime factorization of 200. example of factor-t The prime factorization of 200 is 23 x 52.

Prime Factorization: T's and Tree

The Fundamental Theorem of Arithmetic states that every composite number can be broken down into a unique product of prime numbers. Prime factorization is the process that finds the prime-number products of a given composite number. You may be able to find a number's prime factorization in your head. For example, 12 is 2 x 2 x 3 or 22 x 3. (Prime factorizations are often represented with exponents.)

Which of the following numbers is not divisible by 3? A 4,873 B 7,521 C 12,642 D 25,308

The correct answer is A. The fast way to do this problem is to use the divisibility rule; add the digits of each number looking for the one that is not a multiple of three. The slow way would be to do each division problem—even on a calculator, this method will take longer!

Which of the follwing is a prime number? A 33 B 45 C 41 D 51

The correct answer is C. Forty-one is a prime number; the other numbers are composite. Be careful with 51—it comes from 3 x 17.

Factor Tree

With a factor tree, you are always breaking a number into the product of two numbers until the numbers are prime. There are many tactics for getting started at the top of the tree, which means that the trees will not necessarily look the same when made by different people. Use whatever works best for you to figure out any two numbers that will multiply together to make the number you need. factor tree factor tree Here is another example for the prime factorization of 200. factor tree

Composite numbers

have more than two factors but not an infinite number of factors. All even numbers (except the number two) are composite, since they can all be divided by two. Zero is neither prime nor composite. Since any number times zero equals zero, there are an infinite number of factors for a product of zero. A composite number must have a finite number of factors.

One

neither prime nor composite. The only way to get a product of one is by multiplying 1 x 1. But duplicate factors are only counted once, so one only has one factor. (A prime number has exactly two factors, so one can't be prime.)

Prime number

A positive integer not divisible by any positive integer other than itself and the number one. If you know your divisibility rules (covered in the next section), then determining the prime numbers from 1-100 is a relatively easy task. Here are the prime numbers up to 25: 2, 3, 5, 7, 11, 13, 17, 19, 23

Numbers in Their Prime

All whole numbers are categorized as either prime or composite, with the exceptions of zero and one, which are special cases. Let's take a look at the difference between prime and composite numbers.