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.

no 401 no no no no no no no 409
no no no no no no no no no 419
no 421 no no no no no no no no
no 431 no 433 no no no no no 439
no no no 443 no no no no no 449

4

Factor the following numbers:

1 216

Factor Decomposition

216 = 23 · 33

2 360

Factor Decomposition

360 = 23 · 32 · 5

3 432

Factor Decomposition

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

Factor Decomposition

2,250 = 2 · 32 · 53

2 3,500

Factor Decomposition

3,500 = 22 · 53 · 7

3 2,520

Factor Decomposition

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

Factor Decomposition

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

Factor Decomposition

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

Divisions

GCD (72, 16) = 8

2 656 and 848

Divisions

GCD (656, 848) = 16

3 17,28 and 842

Divisions

GCD (1,278, 842) = 2