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 Pair1 | 12 ÷ 1 = 12 | 1 x 12 |

2 | 12 ÷ 2 = 6 | 2 x 6 |

3 | 12 ÷ 3 = 4 | 3 x 4 |

4 | 12 ÷ 4 = 3 | 4 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 Pair1 | 20 ÷ 1 = 20 | 1 x 20 |

2 | 20 ÷ 2 = 10 | 2 x 10 |

3 | 20 ÷ 3 = 6 R2 | -------- |

4 | 20 ÷ 4 = 5 | 4 x 5 |

5 | 20 ÷ 5 = 4 | 5 x 4 |

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

Example 3: find the factors of 49.

Counting #DivisionFactor Pair1 | 49 ÷ 1 = 49 | 1 x 49 |

2 | 49 ÷ 2 = 24 R1 | -------- |

3 | 49 ÷ 3 = 16 R1 | -------- |

4 | 49 ÷ 4 = 12 R1 | -------- |

5 | 49 ÷ 5 = 9 R4 | -------- |

6 | 49 ÷ 6 = 8 R1 | -------- |

7 | 49 ÷ 7 = 7 | 7 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:

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.ANSWER BOX: GCF = See more: Regulatory And Informational Markers Are Identified Through Which Features 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: |