You are watching: What number between 1 and 20 has exactly 5 factors

Solution: 1 yd x 7 yd

The whole-number dimensions, 1 and also 7, of the rectangle-shaped garden above, room the factors of the number 7.

Problem 2: The area that a rectangular garden is 8 square yards. Perform all feasible whole-number dimensions the garden deserve to have.

Solution: 1 yd x 8 yd, 2 yd x 4 yd

The whole-number dimensions, 1, 2, 4 and 8, the the rectangular gardens in difficulty 2, room the factors of the number 8. In problem 1, the number 7 has only 2 factors. The number 7 is prime. In trouble 2 above, the number 8 has 4 factors. The number 8 is composite.

**Definitions**A

**prime number**has only two factors: 1 and itself.A

**composite number**has more than 2 factors.

**The number 1**is neither prime nor composite.

When the area that a rectangle is a element number, there is just one collection of possible dimensions for that rectangle. As soon as the area of a rectangle is a composite number, there room two or more sets of possible dimensions for the rectangle. Each set of dimensions is a pair that factors.

To identify if a number is prime or composite, follow this steps:

Find all components of the number.If the number has actually only two factors, 1 and also itself, then it is prime.If the number has more than two factors, then it is composite.Example 1: Is the number 2 element or composite?

Solution: The determinants of 2 are 1 x 2. 2 is prime.

Example 2: Is the number 9 element or composite?

Solution: The determinants of 9 space 1 x 9, 3 x 3. 9 is composite.

We have established if a solitary number is prime or composite. Let"s look at a range of numbers to check out if they space prime or composite. Please note that each variety of numbers given in instances 3, 4 and 5 below are inclusive.

Example 3: Find all prime numbers between 2 and also 9.

factors the 2: | 1 x 2 | 2 is prime |

factors that 3: | 1 x 3 | 3 is prime |

factors of 4: | 1 x 4, 2 x 2 | 4 is composite |

factors of 5: | 1 x 5 | 5 is prime |

factors of 6: | 1 x 6, 2 x 3 | 6 is composite |

factors of 7: | 1 x 7 | 7 is prime |

factors the 8: | 1 x 8, 2 x 4 | 8 is composite |

factors that 9: | 1 x 9, 3 x 3 | 9 is composite |

Solution: The element numbers in between 2 and 9 room 2, 3, 5 and also 7.

Example 4: Find all prime numbers in between 10 and 19.

factors the 10: | 1 x 10, 2 x 5 | 10 is composite |

factors of 11: | 1 x 11 | 11 is prime |

factors that 12: | 1 x 12, 2 x 6, 3 x 4 | 12 is composite |

factors the 13: | 1 x 13 | 13 is prime |

factors the 14: | 1 x 14, 2 x 7 | 14 is composite |

factors that 15: | 1 x 15, 3 x 5 | 15 is composite |

factors of 16 | 1 x 16, 4 x 4 | 16 is composite |

factors that 17: | 1 x 17 | 17 is prime |

factors that 18: | 1 x 18, 3 x 6 | 18 is composite |

factors of 19: | 1 x 19 | 19 is prime |

Solution: The element numbers in between 10 and also 19 are 11, 13, 17 and 19.

Example 5: Find every prime numbers between 20 and also 29.

factors the 20: | 1 x 20, 2 x 10, 4 x 5 | 20 is composite |

factors the 21: | 1 x 21, 3 x 7 | 21 is composite |

factors the 22: | 1 x 22, 2 x 11 | 22 is composite |

factors of 23: | 1 x 23 | 23 is prime |

factors that 24: | 1 x 24, 2 x 12, 3 x 8, 4 x 6 | 24 is composite |

factors the 25: | 1 x 25, 5 x 5 | 25 is composite |

factors that 26: | 1 x 26, 2 x 13 | 26 is composite |

factors of 27: | 1 x 27, 3 x 9 | 27 is composite |

factors that 28: | 1 x 28, 2 x 14, 4 x 7 | 28 is composite |

factors the 29: | 1 x 29 | 29 is prime |

Solution: The prime numbers in between 20 and also 29 space 23 and 29.

Example 6: Is the number 31 element or composite? describe your price using full sentences.Solution 1: The number 31 is prime due to the fact that its only determinants are one and itself.

Solution 2: Thirty-one is a element number. This is due to the fact that the number 31 has only 2 factors: 1 and 31.

Solution 3: I divided the number 31 by all numbers in between 1 and 31 and found no components other than one and thirty-one. Therefore, 31 is prime.

There space many feasible ways to define the solution to this problem. These are just three feasible explanations.

Summary: A prime number has only 2 factors: 1 and also itself. A composite number has more than 2 factors. The number 1 is no prime nor composite.

The element numbers in between 2 and 31 space 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and also 31 due to the fact that each of these numbers has only 2 factors, itself and 1.

**Exercises**

Directions: review each question below. Pick your prize by clicking on its button. Feedback to your answer is detailed in the results BOX. If you make a mistake, choose a different button.

1. | Each of the adhering to numbers is composite EXCEPT:30, 31, 32, 33, 34, 35, 36, 37, 38, 3932 and 3930 and also 3431 and also 37All compositeRESULTS BOX: |

2. | The prime numbers in between 40 and 49 are:42, 43 and also 4741, 43 and also 47 43, 45 and also 47None the the above.RESULTS BOX: |

3. | The element numbers between 50 and also 59 are:53 and also 5951 and also 59 53 and also 57None the the above.RESULTS BOX: |

4. | The prime numbers in between 60 and 69 are:63 and 6961 and also 67 60 and also 65None of the above.RESULTS BOX: |

5.See more: How Old Is Lee And Tiffany Filmed? Lee And Tiffany Lakosky Net Worth | The element numbers between 20 and 69 are:21, 23, 29, 31, 37, 41, 43, 47, 53, 63 and also 6923, 29, 31, 33, 37, 41, 43, 47, 59, 61 and 6723, 29, 31, 37, 41, 43, 47, 53, 59, 61 and also 67None the the above.RESULTS BOX: |