Factors and Multiples

Factors/Divisors & Multiples

Uncovering the DNA of these three concepts

FACTORS

Factors are whole numbers that are multiplied together to produce another number. The original numbers are factors of the product number. If a x b = c then a and b are factors of c.

Example:

4 x 7 = 28 (4 and 7 are both factors of 28)

8 x 12 = 96 (8 and 12 are both factors of 96)

...FACTORS

Finding Factors can be easy if you use the double and halfing rule and by using divisibility rules

Example: finding factors of 54

1 x 54

2 x 27 (half of 50 is 25 and half of 4 is 2)

3 x 18 (using divisibility rule of 3, then divide to find other factor)

6 x 9

Factors of 54 = 1,2,3,6,9,18,27,54

...FACTORS

Common Factors are the factors that are shared between two or more numbers. G.C.F. or Greatest Common Factors are the two factors that are the highest shared factors.

Example: Common Factors of 54 and 126

54 = 1,2,3,6,9,18,27,54

126 = 1,2,3,6,7,9,14,18,21,42,63,126

The G.C.F. is 18

...FACTORS

Using the G.C.F (Greatest Common Factor)

Example: Common Factors of 54 and 126

54 = 1,2,3,6,9,18,27,54

126 = 1,2,3,6,7,9,14,18,21,42,63,126

The G.C.F. is 18

Imagine the problem was: Mr. da Silva wants to organize his 54 silver coins and 126 gold coins into packages with the same number of coins in each package. What is the highest number of coins he can place in each package?

MULTIPLES

Multiples are the resulting numbers of skip counting. It is a number that can be divided by another number a certain number of times without a remainder.

5 x 4 = 20 (20 is a multiple of both 4 and 5)

Oh! And by the way 4 and 5 are both factors and divisors.

...MULTIPLES

Noticing simple patterns in multiple counting can help you beyond the 'MULTIPLICATION TABLE'. When skip counting by any number you start to see patterns in units place value or the "start over zone".

Example: Counting by 7s and moving beyond the Multiplication table.

7,14,21,28,35,42,49,56,63,70 *Start over zone*

77,84,91,108,115,122,129,136...

Notice how at 70 you began to use the same digits in the units place. The trick is to find the multiple that ends in zero and that is your "Start over zone"

...MULTIPLES

Common Multiples are the shared results between two different factors. When you skip count by two or more different numbers you will land of common multiples.

Example:

4,8,12,16,20,24,28,32,36,40,44,48

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48

Notice that the common multiples are counting by twelves.

12+12=24+12=36+12=48

...MULTIPLES

L.C.M. or Lowest Common Multiple is a great strategy to find the same multiple between numbers and avoid counting by each number endlessly and uselessly.

4,8,12,16,20,24,28,32,36,40,44,48

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48

L.C.M is 12, so now I can use 12 rather than continue to count by 4 and 3

...MULTIPLES

Here is a problem that can use this strategy:

A drummer hits her snare drum every 4 seconds and his cymbals every 3 seconds. If she plays for 2 minutes and 15 seconds, how many times will she hit the snare drum and the cymbal at the exact same time?

We know that the L.C.M. is 12 so instead of counting by 3 and 4, we can count by 12. Since the song is 75 seconds (2 minutes 15 seconds) we can count by 12 all the way to 75

12,24,36,48,60*,72

She will hit both the snare and cymbal at 6 times simultaneously during a 2 minute and 15 second song.

Multiple Choice

What is the G.C.F between 24 and 32?

• 24

• 32

• 8

• 12

Multiple Select

What is the L.C.M of 3/6/9/12

• 18

• 24

• 12

• 36

Multiple Choice

Sharron lifts weights every 2 days, does yoga every 3 days, does cardio every 5 days and kickboxing every 6 days. During the month of September (30 days) when will she do all 4 workouts on the same day?

• never

• once

• twice

• three times