9G (2.4) PART 1 Factoring

(2.4)
Factoring

Every number has factors.

The factors of a number, for example 10, are the Integers which multiply to get the original number, so the factors of 10 are 1 and 10, 2 and 5

Multiple Select

What are the factors of 10 ?

• 10

  because

  1(10) = 10

• 1

  because

  10(1) = 10

• 5

  because

  2(5) = 10

• 2

  because

  5(2) = 10

• 9

  because

  2(9) = 10

So the factors of 10 are:
1 and 10
2 and 5
or
1,2,5,10

Multiple Select

What are the factors of 15 ?

• 1

  because

  1(15) = 15

• 15

  because

  15(1) = 15

• 3

  because

  5(3) = 15

• 5

  because

  3(5) = 15

• 10

  because

  5(10) = 15

So the factors of 15 are:
1 and 15
3 and 5
or
1,3,5,15

Multiple Select

What are the factors of 21?

• 1

  because

  21(1) = 21

• 21

  because

  1(21) = 21

• 3

  because

  7(3) = 21

• 7

  because

  3(7) = 21

• 11

  because

  2(11) = 21

So the factors of 21 are:
1 and 21
3 and 7
or
1,3,7,21

Multiple Select

What are the factors of 55?

• 1

  because

  55(1) = 55

• 55

  because

  1(55) = 55

• 5

  because

  11(5) = 55

• 11

  because

  5(11) = 55

• 15

  because

  4(15) = 55

So the factors of 55 are:
1 and 55
5 and 11
or
1,5,11,55

Multiple Select

What are the factors of 95?

• 1

  because

  95(1) = 95

• 95

  because

  1(95) = 95

• 5

  because

  19(5) = 95

• 19

  because

  5(19) = 95

• 15

  because

  6(15) = 95

So the factors of 55 are:
1 and 95
5 and 19
or
1,5,19,95

Numbers that only have two factors:
1 and itself, are called prime numbers.

Let's see some more prime numbers

WE can go on forever looking at primes. The most important thing about primes is
They are the building blocks of all numbers. Let's see that.

Multiple Choice

What prime numbers is the number 30 made of?

• $$1\times2\times3\times5$$

• $$1\times2\times3\times7$$

• $$1\times2\times5\times7$$

• $$1\times3\times5\times7$$

• $$1\times2\times3\times11$$

Multiple Choice

What prime numbers is 20 made out of?

• $$1\times2\times2\times5$$

• $$1\times2\times3\times5$$

• $$1\times3\times3\times5$$

• $$1\times2\times11$$

• $$1\times5\times5$$

Multiple Choice

What prime numbers is 40 made out of?

• $$1\times2\times2\times2\times5$$

• $$1\times2\times3\times5$$

• $$1\times3\times3\times5$$

• $$1\times2\times3\times11$$

• $$1\times2\times5\times5$$

Multiple Choice

What prime numbers is 72 made out of?

• $$1\times2\times2\times2\times3\times3$$

• $$1\times2\times3\times5\times7$$

• $$1\times2\times2\times3\times3\times5$$

• $$1\times2\times2\times3\times3\times7$$

• $$1\times2\times3\times5\times7$$

Multiple Choice

What factors do 10 and 15 have in common?

• 9, 12
• 2, 3
• 1, 5
• 7, 8
• 4, 6

Multiple Choice

What factors do the numbers 20 and 30 have in common?

• 7, 14, 21, 28
• 15, 25, 35, 45
• 12, 18, 24, 30
• 3, 4, 6, 8
• 1, 2, 5, 10

Multiple Choice

What factors do the numbers 42 and 48 have in common?

• 1,2,3,6

• 1,2,4,8

• 1,2,6,7

• 10, 12, 14, 16, 18

• 1, 2, 3, 4, 6, 7, 8

Multiple Choice

What factors do the numbers 32 and 50 have in common?

• 5, 6
• 3, 4
• 1, 2
• 9, 10
• 7, 8

Multiple Choice

What factors do the numbers 12 and 24 have in common?

• 1, 2, 3, 4, 6, 12
• 1, 2, 3, 4, 6, 24, 48
• 1, 2, 3, 4, 6, 24
• 1, 2, 3, 4, 5, 6, 8, 12

Multiple Choice

What factors do the numbers 21 and 27 have in common?

• 8, 10
• 5, 6
• 1, 3
• 4, 9
• 2, 7

Multiple Choice

What is the greatest common factor of 15 and 18?

(the biggest factor that both 15 and 18 have)

• 1
• 2
• 4
• 5
• 3

Multiple Choice

What is the greatest common factor of 20 and 24?

(the largest factor that both 20 and 24 have)

• 5
• 2
• 4
• 10
• 15

Multiple Choice

What is the greatest common factor of 10 and 12 ?

(the largest factor that both 10 and 12 have)

• 6
• 5
• 4
• 2
• 3

The Greatest Common Factor (GCF) is often called the Greatest Common Divisor (GCD), the largest number that divides two number evenly

Multiple Choice

What is the largest number that evenly divides both 10 and 12?

$$\frac{10}{number}=integer$$

$$\frac{12}{same\ number}=integer$$

• 2

• 3

• 4

• 5

• 1

Multiple Choice

What is the largest number that evenly divides both 16 and 24?

$$\frac{16}{number}=integer$$

$$\frac{24}{same\ number}=integer$$

• 7

• 8

• 3

• 4

• 6

Multiple Choice

What is the largest number that evenly divides both 28 and 35?

$$\frac{28}{number}=integer$$

$$\frac{35}{same\ number}=integer$$

• 7

• 10

• 8

• 5

• 9

You can find the Greatest Common Divisor on your calculator

​To find the GCD on you calculator:
1) press the MATH button
2) Press the right arrow key and the cursor will shift from MATH to NUM, as pictured to the left.
3) Press 9 or scroll down with the arrow keys until you reach the gcd( option, as pictured to the left.
4) Enter your first number
5) Press the " , " button which is above the 7
6) Enter your second number
7) Press the " ) " button
8) Press the ENTER button (as pictured to the right)

Next time: how do we find factors of a variable