# 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 = 23 · 33

2 360 360 = 23 · 32 · 5

3 432 432 = 24 · 33

## 5

Factor 342 and determine its number of divisors.

342 = 2 · 32 · 19

n = (1 + 1) · (2+1) · (1 + 1) = 12

## 6

Factor the following numbers:

1 2,250 2,250 = 2 · 32 · 53

2 3,500 3,500 = 22 · 53 · 7

3 2,520 2,520 = 23 · 32 · 5 · 7

## 7

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

1428 and 376

428 = 22 · 107

376 = 23 · 47

G.C.D. (428, 376) = 22 = 4

L.C.M. (428, 376) = 23 · 107 · 47 = 40,232

2148 and 156

148 = 22 · 37

156 = 22 · 3 · 13

GCD (148, 156) = 22 = 4

LCM (148, 156) = 22 · 3 · 37 · 13 = 5,772

3600 and 1,000

600 = 23 · 3 · 52

1,000 = 23 · 53

GCD (600, 1,000) = 23 · 52 = 200

LCM (600 , 1,000) = 23 · 3 · 53 = 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 = 23 · 32

108 = 22 · 33

60 = 22 · 3 · 5

GCD (72, 108, 60) = 22 · 3

LCM (72, 108, 60) = 23 · 33 · 5 = 2,160

2 1,048, 7,86 and 3,930 1,048 = 23 · 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) = 23 · 3 · 5 · 131 = 15,720

3 3,120, 6,200 and 1,864 3,210 = 24 · 3 · 5 · 13

6,200 = 23 · 52 · 31

1,864 = 23 · 233

GCD (3,210, 6,200, 1,864) = 23 = 8

LCM (3,210, 6,200, 1,864) = 24 ·3 · 52 · 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