Download presentation

Presentation is loading. Please wait.

1
**Factors, Primes & Composite Numbers**

2
**Definition Product Product – An answer to a multiplication problem.**

7 x 8 = 56 Product

3
Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

4
Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

5
What are the factors? 6 x 7 = 42 6 & 7 7 x 9 = 63 7 & 9 8 x 6 = 48 8 & 6 4 & 9 4 x 9 = 36

6
What are the factors? 42 ÷ 7 = 6 7 63 ÷ 9 = 7 9 48 ÷ 6 = 8 6 9 36 ÷ 9 = 4

7
**7 Definition 7 is prime because the only numbers**

Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

8
**Examples of Prime Numbers**

2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

9
**8 Definition The factors of 8 are 1, 2, 4, 8**

Composite number – a number that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

10
**Examples of Composite Numbers**

4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

11
**Our Lonely 1 One is not a prime nor a composite number.**

It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors. Special Note: One is not a prime nor a composite number.

12
Definition Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 or 2 2 x 3 = 12

13
**How to Do Prime Factorization Using a Factor Tree**

Step 1 – Start with a composite number. 48 Step 2 – Write down a multiplication problem that equals this number or any pair of factors of this number. 6 x 8 = 48

14
**How to Do Prime Factorization Using a Factor Tree**

Step 3 – Find factors of these factors. 6 x 8 = 48 2 x 3 x 2 x 4 = 48

15
**How to Do Prime Factorization Using a Factor Tree**

Step 4 – Find factors of these numbers until all factors are prime numbers. 6 x 8 = 48 2 x 3 x 2 x 4 = 48 2 x 3 x 2 x 2 x 2 = 48

16
**How to Do Prime Factorization Using a Factor Tree**

Step 5 – Write the numbers from least to greatest. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48

17
**How to Do Prime Factorization Using a Factor Tree**

Step 6 – Count how many numbers are the same and write exponents for them. 6 x 8 = 48 2 x 3 x 2 x 2 x 2 = 48 2 x 2 x 2 x 2 x 3 = 48 4 2 x 3 = 48

18
**Prime factor this number**

4 2 x 2 = 4 2 2 = 4

19
**Prime factor this number**

6 2 x 3 = 6

20
**Prime factor this number**

8 2 x 4 = 8 2 x 2 x 2 = 8 3 2 = 8

21
**Prime factor this number**

9 3 x 3 = 9 2 3 = 9

22
**Prime factor this number**

10 2 x 5 = 10

23
**Prime factor this number**

12 3 x 4 = 12 3 x 2 x 2 = 12 2 x 2 x 3 = 12 2 2 x 3 = 12

24
**Prime factor this number**

14 2 x 7 = 14

25
**Prime factor this number**

15 3 x 5 = 15

26
**Prime factor this number**

16 4 x 4 = 16 2 x 2 x 2 x 2 = 16 4 2 = 16

27
**Prime factor this number**

18 3 x 6 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18 2 x 3 = 18 2

28
**Prime factor this number**

20 4 x 5 = 20 2 x 2 x 5 = 20 2 x 5 = 20 2

29
**Prime factor this number**

21 3 x 7 = 21

30
**Prime factor this number**

22 2 x 11 = 22

31
**What about those with variables?**

24y2 We do the same as before, we just add the variables with it 2 * 2 * 2 * 3 * y * y 23 * 3 * y2

32
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70.

33
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10

34
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5

35
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5

36
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5

37
**4-5 Greatest Common Factor**

Example Use prime factorization to find the GCF of 42 and 70. First find the prime factorization of each number. 42 = 7 * = 7 * 10 = 7 * 2 * = 7 * 2 * 5 Then find the common factors. 42 = 7 * 2 * 3 70 = 7 * 2 * 5 The greatest common factor of 42 and 70 is 2 * 7 or 14.

38
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m

39
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m

40
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m

41
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m

42
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m

43
**4-5 Greatest Common Factor**

Example Find the greatest common factor of 6m2 and 15m First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m Then find the common factors. 6m2 = 3 * 2 * m * m 15m = 3 * 5 * m The greatest common factor of 6m2 and 15m is 3 * m or 3m.

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google