Yesterday we learned some divisibility rules and played a game to help us with our prime and composite numbers.
The kids have learned what prime and composite numbers are: Prime numbers- have only two factors, one and itself EXAMPLE) 2- the only two factors that can be multiplied together to make 2 are 1 and 2 (itself) Composite numbers- have 3 or more unique factors (can also stated as "more than 2 unique factors") I am so impressed by how many kids know their math facts this year, however, since we have to learn about prime and composite numbers between 1 and 100, these facts don't always help. One way to figure out how many factors a number has is to just do the division, which could take forever... the student would have to do 89 divided by 2, 89 divided by 3...and so on until they got to 89 divided by 9. Ain't nobody got time for that! So, in order to make it easier to determine a number's factors, we started talking about divisibility rules yesterday. What are divisibility rules? They are rules that tell you if a number is evenly divisible by (can be divided by) a certain number. Here are the rules we follow: 2- A number is divisible by 2 if the number ends in an EVEN number: 0, 2, 4, 6, 8 Examples) 482 is divisible by 2 because the digit in the ones place is an even number. 891 is NOT divisible by 2 because the digit in the ones place is an odd number. 3- A number is divisible by 3 if, after adding up the digits in the number you end up with a sum that is evenly divisible by 3 Examples) 482: 4 + 8 + 2= 14. 14 is not divisible by 3 (when you divide 14 by 3 you have a remainder), so neither is 482. 891 is divisible by 3 because 8 + 9 + 1 = 18 and 18 is evenly divisible by 3 (when you divide 18 into 3 groups, you don't have a remainder). 5- If a number ends in 0 or 5 in the ones place, then the number is divisible by 5. Example) 615 is divisible by 5 because it ends in a 5. 892 is not divisible by 5 because it does not end in a 0 or 5, it ends in 2. 6- If a number is divisible by BOTH 2 and 3, it is also divisible by 6. Example) 624 is divisible by 2 because it ends in an even number in the ones place. 624 is also divisible by 3 because 6 + 2 + 4 = 12 and 12 is divisible by 3 with no remainder. Therefore, 624 is also divisible by 6 because it is divisible by both 2 and 3 (which are factors of 6). 7- Sorry, the rule takes longer to figure out than to just divide whatever number you have by 7 to see if it is a factor. Example) 57 divided by 7 is 8 remainder 1, so it is not divisible by 7. 91 divided by 7 is 13 remainder 0, so it IS divisible by 7, meaning 7 is a factor of 91. 9- Just like the threes rule, if you add up the digits of the number and it is divisible by 9, then the whole number is divisible by 9. Example) 711 added together is 7 + 1 + 1 = 9, and 9 is evenly divisible by 9, so 711 is as well. To find out how many factors a number has, start applying the rules from 2-9 until you find one that works. Once you've figured out even just one additional factor for a number other than 1 and itself, you can automatically stop and call it composite. Example: 93 We know that two factors for 93 are 1 x 93 because all numbers have the factors 1 and itself. Let's test the 2s rule: It is NOT divisible by 2 because it ends in an odd number. So we still only have 2 factors so far: 1 and 93. Let's try the 3s rule: 9 + 3 = 12. 12 is divisible by 3 with no remainder, so that means 93 is as well. Guess what! We don't even need to figure out what the other factor is that has to be multiplied times 3 to get 93- we now know that 3 is a factor because the rule worked, 93 has at least 3 factors- 1,3 and 93, so we know it is composite! We don't even need to go to the 4s rule because we know three factors already- 1, 3, and 93. Of course, it is a lot less work on paper to memorize the 25 prime numbers from 1-100, however, if you don't do this, you can just follow these rules or do all of the math. For those of you who want to memorize the primes from 1-100, here they are: 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 Always remember that 0 and 1 are neither prime nor composite
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