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Prime and Composite Number

Bell Ringer: Page 33 in JBHM binder (DOK 1)

Focus/Introduction: Page 104 Composite Number- a natural number that has more than two factors. Prime Number- a number that has only two factors, 1 and itself.

Have you ever heard of a superprime? A superprime is a number that remains prime even after digits are removed from the right side one at a time. Example: 2391: remove 1 and 239 is prime, remove 9 and 23 is prime, remove 3 and 2 is prime.

Guided Practice: (DOK 1) What is a composite number? (a number having more than two factors) 8 and 4 are examples of composite numbers. What is a prime number? (a number that has only two factors, 1 and itself; 2, 3, 5, and 17 are examples of prime numbers)

Is 1 prime or composite? It is a lonely number because it is neither prime nor composite. It is not a prime number because it does not have exactly two factors, and it is not composite because it does not have more than two factors. So, 1 is not prime or composite.

Divisibility Rules: A number is divisible by ___ if… 2 – The number is an even number, ending in 2, 4, 6, 8, 0. Example: 124: It ends in 4, so it is divisible by ÷ 2 = 62

Divisibility Rules: A number is divisible by ___ if… 3 – The sum of the digits is divisible by 3. Example: 150: The sum of the digits, = 6, is divisible by 3, so 150 is divisible by ÷ 3 = 50

Divisibility Rules: A number is divisible by ___ if… 4 – The number is even and the last 2 digits form a number that is divisible by 4. Example: 724: It is even, and the last two digits, 24, is divisible by 4, so 724 is divisible by ÷ 4 = 181

Divisibility Rules: A number is divisible by ___ if… 5 – The number ends in 0 or 5. Example: 105: It ends in 5, so 105 is divisible by ÷ 5 = 21

Divisibility Rules: A number is divisible by ___ if… 6– The number is even, and the sum of its digits is divisible by 3. Example: 450: It is even and the sum of the digits, = 9, is divisible by 3, so 450 is divisible by 6. In other words, if the rule for 2 and the rule for 3 work, the number is divisible by ÷ 6 = 75

Divisibility Rules: A number is divisible by ___ if… 7 and 8 – These rules are too complicated to actually be shortcuts.

Divisibility Rules: A number is divisible by ___ if… 9 – The sum of the digits is divisible by 9. Example: 450: The sum of the digits, = 9, is divisible by 9, so 450 is divisible by ÷ 9 = 50

Divisibility Rules: A number is divisible by ___ if… 10 –The number ends in 0. Example: 1250: It ends in 0, so 1250 is divisible by ÷ 10 = 125

Independent Practice/Activities: (DOK 2) Divisibility Practice: Is the first number divisible by the second? Explain “why” or “why not.”

1.825; 5___ 2.91; 2___ 3.51; 3____ 4.39; 3___ 5.726; 6___ 6.117; 3____

7. 100; 5___ ; 6___ 9. 40; 10___ ; 3___ ; 3___ ; 9___ ; 2___ ; 4___

Which of the numbers are prime or composite? (DOK 1) 1.825— 2.17— 3.91— 4.25— 5.51— 6.1— 7.39— 8.29—

Closure: Who can explain prime/composite numbers. Homework: List the prime numbers 1—25.