Problem: The area that a rectangle-shaped garden is 24 square yards. Perform all feasible whole-number dimensions the garden deserve to have.

You are watching: Common factors of 20 and 24

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Solution: 1 yd x 24 yd, 2 yd x 12 yd, 3 yd x 8 yd, and 4 yd x 6 yd

The whole-number dimensions of this rectangular garden room the factors of the number 24. The following statements deserve to be made around the factors of 24:

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24 because each of this numbers divides precisely into 24.The pairs the factors of 24 are: 1 and 24, 2 and 12, 3 and 8, and 4 and also 6.

To uncover the factors of a whole number follow this procedure:

Keep splitting until a factor repeats.List all determinants separated by commas.

Example 1: find the determinants of 12.

Counting # DivisionFactor Pair
112 ÷ 1 = 121 x 12
212 ÷ 2 = 62 x 6
312 ÷ 3 = 43 x 4
412 ÷ 4 = 34 x 3 

Solution: The factors of 12 room 1, 2, 3, 4, 6 and 12.

(Note: 

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 means the one or an ext factors has repeated so we avoid dividing.)

Example 2: find the components of 20.

Counting #DivisionFactor Pair
120 ÷ 1 = 201 x 20
220 ÷ 2 = 102 x 10
320 ÷ 3 = 6 R2--------
420 ÷ 4 = 54 x 5
520 ÷ 5 = 45 x 4 

Solution: The components of 20 space 1, 2, 4, 5, 10 and 20.

Example 3: find the factors of 49.

Counting #DivisionFactor Pair
149 ÷ 1 = 491 x 49
249 ÷ 2 = 24 R1--------
349 ÷ 3 = 16 R1--------
449 ÷ 4 = 12 R1--------
549 ÷ 5 = 9 R4--------
649 ÷ 6 = 8 R1--------
749 ÷ 7 = 77 x 7 

Solution: The components of 49 space 1, 7 and also 49

Problem: discover the Greatest usual Factor (GCF) the 12 and also 20. (Note: place your mouse over the lists of factors below.)

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The typical factors the 12 and 20 room 1, 2 and 4.

The greatest common aspect of 12 and also 20 is 4.

Solution: GCF = 4

To uncover the Greatest common Factor (GCF) of two or more whole numbers, monitor this procedure:

Make a list of factors for each totality number.Identify all components that are typical to all lists.The Greatest typical Factor (GCF) is the biggest of these typical factors.In examples 4 v 6, place your computer mouse over the perform of components to see the typical factors.

Example 4: find the GCF the 24 and also 36.

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The usual factors that 24 and 36 are 1, 2, 3, 4, 6 and also 12.

The greatest common aspect of 24 and also 36 is 12.

Solution: GCF = 12

Example 5: find the GCF that 56 and 63.

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The usual factors of 56 and also 63 room 1 and also 7.

The greatest common element of 56 and 63 is 7.

Solution: GCF = 7

Example 6: discover the GCF of 12, 30 and 54.

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The usual factors that 12, 30 and 54 room 1, 2, 3 and also 6.

The greatest common element of 12, 30 and 54 is 6.

Solution: GCF = 6

Summary: The components of a entirety number are those numbers the divide specifically into that totality number. The Greatest usual Factor (GCF) the a collection of whole numbers is the biggest factor common to all totality numbers in the set.

Exercises

Directions: review each inquiry below. Click when in response BOX and form in your answer; climate click ENTER. After friend click ENTER, a article will appear in the outcomes BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1.Find the GCF the 18 and also 36.ANSWER BOX: GCF =   

RESULTS BOX: 

2.Find the GCF of 30 and 48.ANSWER BOX: GCF =   

RESULTS BOX: 

3.Find the GCF of 42 and also 56.ANSWER BOX: GCF =   

RESULTS BOX: 

4.Find the GCF the 16, 48 and 72.

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ANSWER BOX: GCF =   

RESULTS BOX: 

5.One rectangular garden has an area the 18 square meters. An additional rectangular garden has actually an area the 81 square meters. What is the largest possible whole-number dimension common to both gardens?ANSWER BOX: GCF =  m  

RESULTS BOX: