Question 12138: Hello-
I need,(in a 6th grade defintion),help on DIVISIBILTY, and PRIME AND COMPOSITE NUMBERS!! It would help If you could explain the rules for:
2,5,10,and,3. and If possible type a short list of PRIME NUMBERS, and, COMPOSITE NUMBERS!.< My teacher didn't explain this in an eaasy way...LOL!!
The worksheet is divided into four boxes, and in each box, I need to find all the numbers divisible by: 2,5,10,3. In each box I need to color in the numbers to create a picture!! THIS IS SO CUNFUSING!!!!
NEED HELP ASAP!!!!
Sincerely,
-Anonymous
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The following is an excerpt from my book Basic Algebra: One Step at a Time. I may later convert it to a Lesson Plan with algebra.com, but for now here is something that may answer some of your question.
R^2 at SCC
Each of the numbers 15, 18, 26, and 91 could be written as the product of smaller numbers. What if you were asked to factor 17? What about 37? You will not be able to find smaller numbers that can be used to break down the 17 or the 37, as you did with 15, 18, 26, and 91. Since the numbers 17 and 37 cannot be expressed as the product of smaller numbers, they are called prime numbers. A prime number is any number larger than 1 that has exactly two factors: 1 and itself. A composite number is any number that has more than two factors. Composite numbers may be broken down into the product of smaller numbers. The number 1 is a special number in that it is neither prime nor composite.
DEFINITIONS
A prime number is a number larger than 1 that cannot be
expressed as the product of two smaller numbers.
A composite number is a number that can be expressed as
the product of two smaller numbers.
The number one (1) is neither prime nor composite.
Complete the following list of prime numbers from 2 to 101:
Complete the following list of prime numbers from 2 to 101.
2, 3, ___, ___, ___, ___, ___, 19, ___, ___, ___, ___, 41,
___, ___, ___, 59, ___, ___, 71, ___, ___, ___, 89, ___, 101.
Perhaps you noticed that the larger the numbers, the harder it its to tell whether or not the numbers are prime. At this point, it will be helpful to learn a few shortcuts to determine divisibility by certain numbers. With or without these shortcuts, a calculator will be very helpful.
1. Divisibility using a calculator. To determine if a number is divisible by a second number with a calculator, just divide the first number by the second number to see if it comes out a whole number on the calculator. For example, to see if 5289 is divisible by 41, type [5289] [] [41] [=]. You will see that the answer is the whole number 129. Is 5289 divisible by 73? When you divide, the answer is NOT a whole number, but rather it comes out to a decimal (like 72.45205 and more!). Thus you can see that 5289 is NOT divisible by 73.
2. Divisibility by 2. What numbers are divisible by 2? You probably already know the answer even numbers, numbers whose last digit is even.
3. Divisibility by 5. What numbers are divisible by 5? Again, you probably already know the answer--numbers that end in a 5 or a 0.
4. Divisibility by 10. What numbers are divisible by 10? Again, you already know this--numbers that end in a 0.
5. Divisibility by 3. What numbers are divisible by 3? Look at some numbers that you know are divisible by 3, like 15, 18, 33, 42, 66, 72, and 75 to name a few. Notice that in every case, the sum of the digits is also divisible by 3. On the other hand, try some numbers like 13, 26, 41, 43, 44, etc. that are not divisible by 3. Notice that the sum of the digits also is not divisible by 3.
6. Divisibility by 9. Look at some numbers that you know are divisible by 9: 18, 27, 36, 45, 54, 63, 72, 81, and 90. Notice that in every case, the sum of the digits is also divisible by 9. On the other hand, try some numbers like 12, 26, 48, 53, 84, etc. that are not divisible by 9. Notice that the sum of the digits also is not divisible by 9.
DIVISIBILITY BY 3 AND 9
If a number is divisible by 3 or by 9, then the sum of its digits is also divisible by 3 or by 9, and vice-versa.
If the sum of the digits is not divisible by 3 or by 9, then the number is not divisible by 3 or by 9, and vice-versa.
NOTICE THAT THIS RULE ONLY WORKS FOR 3 AND 9.
7. Divisibility by 4. If the last two digits are divisible by 4, then the number is divisible by 4.
8. Divisibility by 6. To be divisible by 6, a number must be divisible by 2 and also by 3. In other words, it must be an even number that is divisible by 3.
You probably noticed that for larger numbers it becomes more difficult to determine if the number is prime. For very large numbers it becomes very difficult. As a general rule, to determine if a number is prime, you must check to see if any prime numbers up to and including the square root of the number divide into it evenly. For example, to determine if 97 is a prime number, first use your calculator to find the square root of 97, which is 9.8. Then check to see if 97 is divisible by any prime number up to 9.8--that is, 2,3,5, or 7.
EXCERPT from Basic Algebra: One Step at a Time, by Dr. Robert J. Rapalje
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