You are watching: Is 30 a prime or composite number

Solution: 1 yd x 7 yd

The whole-number dimensions, 1 and also 7, that the rectangular garden above, space the factors of the number 7.

Problem 2: The area that a rectangular garden is 8 square yards. Perform all possible whole-number size 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, that the rectangular gardens in difficulty 2, space the determinants of the number 8. In trouble 1, the number 7 has only two factors. The number 7 is prime. In problem 2 above, the number 8 has 4 factors. The number 8 is composite.

**Definitions**A

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

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

**The number 1**is no prime nor composite.

When the area that a rectangle is a element number, over there is only one set of possible dimensions for the rectangle. As soon as the area that a rectangle is a composite number, there are two or an ext sets of possible dimensions for the rectangle. Each collection of dimensions is a pair of factors.

To recognize if a number is prime or composite, follow these steps:

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

Solution: The components of 2 room 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 determined if a solitary number is element or composite. Let\"s look at a variety of numbers to watch if they are prime or composite. Please note that each variety of numbers provided in examples 3, 4 and also 5 below are inclusive.

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

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

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

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

factors that 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 of 8: | 1 x 8, 2 x 4 | 8 is composite |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solution 2: Thirty-one is a prime number. This is because the number 31 has actually only 2 factors: 1 and also 31.

Solution 3: I separated the number 31 by every numbers between 1 and also 31 and also found no factors other 보다 one and also thirty-one. Therefore, 31 is prime.

There space many feasible ways to explain the systems to this problem. These are just three feasible explanations.

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

The element numbers in between 2 and also 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and also 31 because each of this numbers has only 2 factors, itself and 1.

**Exercises**

Directions: review each question below. Choose your answer by clicking its button. Feedback to your answer is detailed in the outcomes BOX. If you make a mistake, choose a various button.

1. | Each the the following numbers is composite EXCEPT:30, 31, 32, 33, 34, 35, 36, 37, 38, 3932 and also 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 47None the the above.RESULTS BOX: |

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

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

5.See more: How Are Sound Energy And Light Energy Similar, How Are Sound Energy And Light Energy The Same | The prime 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 67None the the above.RESULTS BOX: |