Problem: The area of a rectangular garden is 24 square yards. List all feasible whole-number dimensions the garden have the right to have actually.

You are watching: What are the common factors of 24 and 36

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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 are the factors of the number 24. The adhering to statements can be made about the factors of 24:

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

To discover the components of a entirety number follow this procedure:

Keep splitting until a element repeats.List all components 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 determinants of 12 are 1, 2, 3, 4, 6 and also 12.

(Note: 

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 indicates that one or more factors has repetitive so we soptimal separating.)

Example 2: Find the determinants 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 are 1, 2, 4, 5, 10 and also 20.

Example 3: Find the determinants 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 are 1, 7 and also 49

Problem: Find the Greatest Usual Factor (GCF) of 12 and also 20. (Note: Place your mouse over the lists of components listed below.)

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The common determinants of 12 and 20 are 1, 2 and 4.

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

Solution: GCF = 4

To find the Greatest Typical Factor (GCF) of 2 or more entirety numbers, follow this procedure:

Make a list of components for each whole number.Identify all factors that are common to all lists.The Greatest Common Factor (GCF) is the biggest of these common components.In Examples 4 via 6, location your computer mouse over the lists of determinants to check out the widespread components.

Example 4: Find the GCF of 24 and 36.

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The widespread determinants of 24 and 36 are 1, 2, 3, 4, 6 and also 12.

The greatest widespread factor of 24 and 36 is 12.

Solution: GCF = 12

Example 5: Find the GCF of 56 and also 63.

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The common factors of 56 and also 63 are 1 and 7.

The greatest widespread element of 56 and also 63 is 7.

Solution: GCF = 7

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

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The common factors of 12, 30 and also 54 are 1, 2, 3 and 6.

The greatest prevalent variable of 12, 30 and also 54 is 6.

Solution: GCF = 6

Summary: The components of a totality number are those numbers that divide exactly into that totality number. The Greatest Typical Factor (GCF) of a set of totality numbers is the biggest variable widespread to all entirety numbers in the set.

Exercises

Directions: Read each question listed below. Click once in an ANSWER BOX and form in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to suggest whether your answer is correct or incorrect. To begin over, click CLEAR.

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

RESULTS BOX: 

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

RESULTS BOX: 

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

RESULTS BOX: 

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

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ANSWER BOX: GCF =   

RESULTS BOX: 

5.One rectangular garden has an area of 18 square meters. Another rectangular garden has a space of 81 square meters. What is the largest feasible whole-number dimension common to both gardens?ANSWER BOX: GCF =  m  

RESULTS BOX: