March 3, 2020

Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9

## Exercise 1

## Exercise 2

For the following numbers: 179, 311, 848, 3,566, 7,287, indicate which are prime and which composite numbers.

## Exercise 3

Determine, using a table, all the prime numbers between 400 and 450.

## Exercise 4

Factor the following numbers:

- 216
- 360
- 432

## Exercise 5

Factor 342 and determine its number of divisors.

## Exercise 6

Factor the following numbers:

- 2,250
- 428 and 376
- 3,500
- 2,520

## Exercise 7

Calculate the greatest common divisor (GCD) and the lowest common multiple (LCM) of the following numbers:

- 148 and 156
- 600 and 1,000

## Exercise 8

Calculate the greatest common divisor (GCD) and the lowest common multiple (LCM) of the following numbers:

- 72, 108 and 600
- 1,048, 786 and 3,930
- 3,120, 6,200 and 1,864

## Exercise 9

Determine, using the Euclidean algorithm, the greatest common divisor (GCD) of the following:

- 72 and 16
- 656 and 848
- 1,278 and 842

## Solution of exercise 1

816, 833, 850

## Solution of exercise 2

For the following numbers: 179, 311, 848, 3,566, 7,287, indicate which are prime and which composite numbers.

Prime numbers: 179 and 311 because each has only two multiples, 1 and the number itself.

Composite numbers : 848, 3,566 and 7,287. These numbers have more than two multiples, so we have categorized them as composite numbers.

## Solution of exercise 3

Determine, using a table, all the prime numbers between 400 and 450.

401 | 409 | ||||||||

419 | |||||||||

421 | |||||||||

431 | 433 | 439 | |||||||

443 | 449 |

## Solution of exercise 4

Factor the following numbers:

- 216

2 | 216 |
---|---|

2 | 108 |

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

2. 360

2 | 360 |
---|---|

2 | 180 |

2 | 90 |

3 | 45 |

3 | 15 |

5 | 5 |

1 |

3. 432

2 | 432 |
---|---|

2 | 216 |

2 | 108 |

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

3 | 1 |

## Solution of exercise 5

Factor 342 and determine its number of divisors.

## Solution of exercise 6

Factor the following numbers:

- 2,250

2 | 2250 |
---|---|

3 | 1125 |

3 | 375 |

5 | 125 |

3 | 21 |

7 | 7 |

1 |

2. 3,500

2 | 3500 |
---|---|

2 | 1750 |

5 | 875 |

5 | 175 |

5 | 35 |

7 | 7 |

1 |

3. 2,520

2 | 2520 |
---|---|

2 | 1260 |

2 | 630 |

3 | 315 |

3 | 105 |

5 | 35 |

7 | 7 |

1 |

## Solution of exercise 7

Calculate the greatest common divisor (GCD) and the lowest common multiple (LCM) of the following numbers:

1. 428 and 376

G.C.D.

L.C.M.

2. 148 and 156

GCD

LCM

3. 600 and 1,000

GCD

LCM

## Solution of exercise 8

1. 72, 108 and 60.

GCD

LCM

2 | 1048 |
---|---|

2 | 524 |

2 | 262 |

131 | 131 |

1 |

2 | 786 |
---|---|

3 | 393 |

131 | 131 |

1 |

2 | 3930 |
---|---|

3 | 1965 |

5 | 655 |

131 | 131 |

1 |

3. 3,120, 6,200 and 1,864

2 | 3120 |
---|---|

2 | 1560 |

2 | 780 |

2 | 390 |

5 | 195 |

3 | 39 |

13 | 13 |

1 |

2 | 6200 |
---|---|

2 | 3100 |

2 | 1550 |

5 | 775 |

5 | 155 |

31 | 31 |

1 |

2 | 1864 |
---|---|

2 | 932 |

2 | 416 |

2 | 208 |

2 | 104 |

2 | 52 |

2 | 26 |

13 | 13 |

1 |

GCD

LCM

## Solution of exercise 9

Determine, using the Euclidean algorithm, the greatest common divisor (GCD) of:

1. 72 and 16

GCD (72, 16) = 8

GCD (656, 848) = 16

3. 17,28 and 842

GCD (1,278, 842) = 2