Question

Enter T or F depending on whether the statement is a true proposition or not. (You must enter T or F -- True and False will not work.) F 1. 290 is divisible by 17 T2. 360 divides 20 F3. 16 divides 208 F4. 10∣181 F5. 17 divides 171 F6. 176∣16 F7. 33653 is divisible by 188 F8. 17878 is divisible by 177 F9. 13∣221

Answer 1

(1) F (5) F (9) T

(2) F (6) F

(3) T (7) F

(4) F (8) F

Explanation:

(1)

290 is divisible by 17.

`(290)/(17)=(17*17)+1`

On dividing 290 by 17 there is a remainder left, i.e. 1.

Thus, this statement is False, F.

(2)

360 divides 20.

`(20)/(360)=(1)/(18)`

On dividing 20 by 360 the result are in fractions.

Thus, this statement is False, F.

(3)

16 divides 208.

`(208)/(16)=(13*16)+0`

On dividing 208 by 16 there is no remainder left.

Thus, this statement is True, T.

(4)

10 | 181

`(181)/(10)= (18*10)+1`

On dividing 181 by 10 there is a remainder left, i.e. 1.

Thus, this statement is False, F.

(5)

17 divides 171

`(171)/(17) =(17*10)+1`

On dividing 171 by 17 there is a remainder left, i.e. 1.

Thus, this statement is False, F.

(6)

176 | 16

`(16)/(176)= (1)/(11)`

On dividing 16 by 176 the result are in fractions.

Thus, this statement is False, F.

(7)

33653 is divisible by 188

`(33653)/(188) =(179*188)+1`

On dividing 33653 by 188 there is a remainder left, i.e. 1.

Thus, this statement is False, F.

(8)

17878 is divisible by 177

`(17878)/(177) =(101*177)+1`

On dividing 17878 by 177 there is a remainder left, i.e. 1.

Thus, this statement is False, F.

(9)

13 | 221

`(221)/(13)= (17*13)+0`

On dividing 221 by 13 there is no remainder left.

Thus, this statement is True, T.