GCF: Common Factors and The Greatest Common Factor

Common Factors

Let us say you have worked out the factors of two or more numbers:

Common Factors of 12 and 30

Factors of 12: 1, 2, 3, 4, 6 and 12

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

The common factors are those that are found in both lists: 1, 2, 3, and 6

It is a common factor when it is a factor of two or more numbers.
(It is then "common to" those numbers.)

Greatest Common Factor: GCF

The GCF is the largest common factor of two or more numbers. 

In the example above, 6 is the GCF because it is the largest factor.

Greatest Common Factor of 12 and 30

Factors of 12: 1, 2, 3, 4, 6 and 12

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

GCF of more than two numbers

Here is another example with three numbers:

Greatest Common Factor of 15, 30 and 105

Factors of 15 are 1, 3, 5, and 15

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105

The factors that are common to all three numbers are 1, 3, 5 and 15

The Greatest Common Factor is 15. 

When do we use this?

Being able to find the GCF is an important skill. We can use the GCF when we are putting a fraction into lowest terms.

Even though 2, 4, and 8 are all common factors, 8 is the GCF and helps you reduce quicker.

Important Note: Greatest Common Factor is sometimes called the Greatest Common Divisor.

LCM: Common Multiples and The Least Common Multiple

Common Multiples

When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers.

For example, when you write down the multiples of 4 and 5, the common multiples are those that are found in both lists:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

Notice that 20 and 40 appear in both lists? 

So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)

Least Common Multiple (LCM)

It is the smallest of the common multiples.

In the last example, the smallest of the common multiples is 20 ...

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

... so the Least Common Multiple of 4 and 5 is 20.

LCM of more than two numbers.

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How to Divide with Decimals

Divisor: Outside number;  Dividend: Inside number;  Quotient: Answer

1. Make the divisor (outside number) a whole number by shifting the decimal to the right. 
2. Move the decimal in the dividend to the right the same number of times. (Note, the dividend might not become a whole number)
3.  Pop the decimal straight up from the dividend onto the line.
4. Ignore the decimal and divide. (do NOT move the decimal in the quotient at the end)

Video Example: 31.773 ÷ 5.1 =

                                   Video Example: 31.773 ÷ 5.1 =

Example: 19.5 ÷ 1.3 =

1.) Make the divisor a whole number . (1.3 became 13) 

2.) Move the decimal in the dividend  to the right the same number of times. (19.5 became 195) 

3.) Pop the decimal straight up from the dividend onto the line. (195 became a whole number, so we did not need a decimal on the line)

4.) Ignore the decimal and divide. (do NOT move the decimal in the quotient at the end)

Example: 2.604 ÷ 8.4 =

This example is from www.enchantedlearning.com.

Example: 48.5 ÷ 1.5 =

Notice how this quotient is a repeating decimal!

This example is from www.enchantedlearning.com.

Example: 6.85 ÷ .5 =

This example is from www.coolmath.com.

How to Multiply Decimals

1. Ignore the decimals and multiply the two numbers as whole numbers.
2. Put the decimal back in the answer.
• Count up how many digits are after the decimal point in both numbers you are multiplying. The answer should have that many numbers after its decimal point. 

                                                       1.2 × 6.04 =

1. Ignore the decimals and multiply the two numbers as whole numbers.  604 × 12 = 7248
• Hint: it is easier if you put the number with more digits on top.   
2. Put the decimal back in the answer.   6.04 has 2 decimal places and 1.2 has 1 decimal place, so the answer has 3 decimal places:    1.2 × 6.04  = 7.248

                                                                                       

                                                    6.04     2 decimal places

                                                 x   1.2     1 decimal place

                                                    1208

                                                 + 6040

                                                    7.248   3 decimal places


                                                                       

                                                                                   .14 × .47=
                                                                                

                                                      .14    2 decimal places

                                                   x .47    2 decimal place

                                                       98

                                                  + 560

                                                  .0658    4 decimal places 

(We had to include a 0 in the tenths place when we put back the decimal because we had to move 4 decimal places)

Multiplying a Decimal by a Decimal Videos

Example 1: 1.34 x 9.8= 

Example 2: .34 x .23=

Example 3: 32.12 x 0.5=

Multiplying a Decimal by a Whole Number Video

Example 4: 2.735 x 4=