# Divisibility Worksheet

### Solutions

1Determine all of the multiples of 17 that exist between 800 and 860.

2For the following numbers: 179, 311, 848, 3,566, 7,287, indicate which are prime and which composite numbers.

3Determine, using a table, all the prime numbers between 400 and 450.

4Factor the following numbers:

1 216

2 360

3 432

5Factor 342 and determine its number of divisors.

6Factor the following numbers:

1 2,250

1428 and 376

2 3,500

3 2,520

7Calculate the greatest common divisor (GCD) and the lowest common multiple (LCM) of the following numbers:

2148 and 156

3600 and 1,000

8Calculate the greatest common divisor (GCD) and the lowest common multiple (LCM) of the following numbers:

1 72, 108 and 60

2 1,048, 786 and 3,930

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

9Determine, usingthe Euclidean algorithm, the greatest common divisor (GCD) of:

1 72 and 16

1 656 and 848

1 1,278 and 842

## 1

Determine all of the multiples of 17 that exist between 800 and 860.

816, 833, 850

## 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.

Composite numbers : 848, 3,566 and 7,287.

## 3

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

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

419 | |||||||||

421 | |||||||||

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

443 | 449 |

## 4

Factor the following numbers:

1 216

216 = 2^{3} · 3^{3}

2 360

360 = 2^{3} · 3^{2} · 5

3 432

432 = 2^{4 } · 3^{3 }

## 5

Factor 342 and determine its number of divisors.

342 = 2 · 3^{2} · 19

n = (1 + 1) · (2+1) · (1 + 1) = 12

## 6

Factor the following numbers:

1 2,250

2,250 = 2 · 3^{2} · 5^{3}

2 3,500

3,500 = 2^{2} · 5^{3} · 7

3 2,520

2,520 = 2^{3 } · 3^{2 } · 5 · 7

## 7

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

1428 and 376

428 = 2^{2} · 107

376 = 2^{3} · 47

G.C.D. (428, 376) = 2^{2} = 4

L.C.M. (428, 376) = 2^{3} · 107 · 47 = 40,232

2148 and 156

148 = 2^{2} · 37

156 = 2^{2} · 3 · 13

GCD (148, 156) = 2^{2} = 4

LCM (148, 156) = 2^{2} · 3 · 37 · 13 = 5,772

3600 and 1,000

600 = 2^{3} · 3 · 5^{2}

1,000 = 2^{3} · 5^{3}

GCD (600, 1,000) = 2^{3} · 5^{2} = 200

LCM (600 , 1,000) = 2^{3} · 3 · 5^{3 }= 3,000

## 8

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

1 72, 108 and 60.

72 = 2^{3 } · 3^{2}

108 = 2^{2 } · 3^{3}

60 = 2^{2 } · 3 · 5

GCD (72, 108, 60) = 2^{2 } · 3

LCM (72, 108, 60) = 2^{3 } · 3^{3} · 5 = 2,160

2 1,048, 7,86 and 3,930

1,048 = 2^{3 } · 131

786 = 2 · 3 · 131

3,930 = 2 · 3 · 5 · 131

GCD (1,048, 786, 3,930) = 2 · 131 = 262

LCM (1,048, 786, 3,930) = 2^{3 } · 3 · 5 · 131 = 15,720

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

3,210 = 2^{4 } · 3 · 5 · 13

6,200 = 2^{3 } · 5^{2 } · 31

1,864 = 2^{3 } · 233

GCD (3,210, 6,200, 1,864) = 2^{3} = 8

LCM (3,210, 6,200, 1,864) = 2^{4} ·3 · 5^{2 } · 13 · 31 · 233 =

= 112,678,800

## 9

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

1 72 and 16

GCD (72, 16) = 8

2 656 and 848

GCD (656, 848) = 16

3 17,28 and 842

GCD (1,278, 842) = 2