Problem: The area of a rectangle-shaped garden is 24 square yards. Perform all possible whole-number dimensions the garden can have.

You are watching: Common factors of 24 and 36

*
*

*
*

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 size of this rectangular garden are the factors of the number 24. The following statements have the right to be made around the determinants of 24:

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

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

Keep dividing until a element repeats.List all determinants separated by commas.

Example 1: uncover the factors 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: 

*
 means the one or much more factors has repeated for this reason we protect against dividing.)

Example 2: find the factors 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 room 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 determinants of 49 are 1, 7 and 49

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

*

The usual factors that 12 and also 20 are 1, 2 and also 4.

The greatest common element of 12 and 20 is 4.

Solution: GCF = 4

To uncover the Greatest usual Factor (GCF) of two or an ext whole numbers, monitor this procedure:

Make a list of factors for each totality number.Identify all determinants that are typical to every lists.The Greatest usual Factor (GCF) is the largest of these typical factors.In instances 4 with 6, location your computer mouse over the lists of factors to see the typical factors.

Example 4: uncover the GCF of 24 and 36.

*

The common factors that 24 and 36 space 1, 2, 3, 4, 6 and also 12.

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

Solution: GCF = 12

Example 5: find the GCF that 56 and also 63.

*

The usual factors that 56 and 63 are 1 and also 7.

The greatest common variable of 56 and also 63 is 7.

Solution: GCF = 7

Example 6: uncover the GCF that 12, 30 and also 54.

*

The usual factors of 12, 30 and 54 are 1, 2, 3 and 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 that divide precisely into that whole number. The Greatest common Factor (GCF) the a set of whole numbers is the biggest factor typical to all totality numbers in the set.

Exercises

Directions: read each question below. Click when in solution BOX and type in her answer; then click ENTER. After girlfriend click ENTER, a blog post will show up in the outcomes BOX to indicate whether your answer is exactly or incorrect. To begin over, click CLEAR.

1.Find the GCF the 18 and 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 of 16, 48 and 72.

See more: Regulatory And Informational Markers Are Identified Through Which Features

ANSWER BOX: GCF =   

RESULTS BOX: 

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

RESULTS BOX: