Prime Numbers and Composite Numbers

Skylar and Henry are returning from the farmer’s market with some new seeds. They were tired of always planting the same old things and wanted something that would really make their garden SING. As they got ready to plant, Skylar remembered what the merchant had told them. In order for your garden to really perform, you must plant these seeds in harmony. Prime number seeds stay together on one side and composite number seeds stay on the other. To work out which seeds should be planted together, we will need to help Sklyar and Henry determine ” Prime and Composite Numbers.” All numbers, starting with one, that we use for counting are called NATURAL NUMBERS. Natural numbers can be divided into two groups based on the number of factors they have. Prime numbers are the first group of natural numbers. A prime number is any number that has ONLY TWO factors: the number one and itself. "The other type of natural numbers are called composite numbers." A composite number is any number that has more than two factors. We can use our number sense, or knowledge of numbers, to determine if a number is prime or composite. Let’s look at the bags of seeds Skylar and Henry bought. The first bag contains seven seeds. Using number sense, how many ways can we evenly group these seeds in the garden? We can plant these seeds in one row of seven. Are there any other numbers we can multiply to get seven? No, since there are only two factors, one and seven, that make seven. Would we say seven is a prime or composite number?

The next bag has nine seeds inside. What is the first set of factors that we know make nine? We know that one times nine equals nine, so one and nine are factors. Are there any other numbers that group nine evenly? We can group nine into three rows of three, so three is a factor of nine. The factors of nine are one, three, and nine. Is nine a prime or composite number? Nine has three factors, so we say it is a COMPOSITE number. This bag is filled with fifty seeds. How can we determine if this number is prime or composite? We can see if there are more than two factors that make fifty. A number can always be made with one and itself, so we know that we can group by one times fifty. What else do we know about fifty that can help determine if it has more factors? "Fifty ends in a zero, so we know that it can be grouped by fives." Five times what would make fifty? Five times ten. Since fifty has more than two factors, fifty is a composite number. Fifty has more factors than what we found. Can you list all the factors of fifty? Write all the factors of fifty below in the comment section.

One last bag of seeds. This one has sixty-one seeds inside. Start with what we know. We know all natural numbers can be made by the factors of one and itself. Can we group sixty-one evenly in another way? No, if we try to group sixty-one by any other factor, there will always be a remainder. Is sixty-one, a prime or composite number? Sixty-one is a prime number. Skylar notices one seed stuck to her tail. She wondered where they were supposed to plant this one. The only way to make one is by multiplying one by itself, but that’s not two factors, so it CAN'T be prime. And since there aren’t any other factors, it CAN'T be composite either. One is a special natural number because it is the only number that is neither prime nor composite. Skylar took this special seed and planted it in a pot! Remember, natural numbers are all counting numbers starting with one. They can be prime or composite. Prime numbers only have TWO factors, one and itself. "Composite numbers have MORE THAN two factors." One is a special number because it's NEITHER prime nor composite. OH! Can you hear that? What is that sound?