**EXERCISE 5 (B)**

**Question 1**

**Which of the following numbers are divisible by 2 ?**

**57, 4, 60, 93, 126, 365, 80, 992**

Sol:

A numbers is divisible by 2 , if their unit digit is even (0 , 2 , 4 , 6 , 8) . So , the answer is 34 , 60 , 126 , 890 , 992 because all these number have even unit digits like 4 , 0 , 6 , 0 , 2 respectively .

**Question 2**

**Which of the following numbers are divisible by 3 ?**

**42, 73, 84, 105, 314, 726, 814, 915**

Sol :

⇒A number is divisible by 3 if the sum of its digits is divisible by 3 i.e.

⇒42 = 4+2 = 6 ÷ 3 (which is divisible by 3 and leaves no remainder)

⇒84 = 8+4 = 12 ÷ 3 (which is divisible by 3 and leaves no remainder)

⇒105 = 1 + 0 + 5 = 6 ÷ 3 (which is divisible by 3 and leaves no remainder)

⇒726 = 7 + 2 + 6 = 15 ÷ 3 (which is divisible by 3 and leaves no remainder)

⇒915 = 9 + 1 + 5 = 15 ÷ 3 (which is divisible by 3 and leaves no remainder)

**Question 3**

**Which of the following numbers are divisible by 5 ?**

**30, 49, 75, 210, 305, 640, 704, 985**

Sol :

⇒A number is divisible by 5 if its unit digit is either 0 or 5

⇒So answer is 30 , 75 , 210 , 305 , 640 , 985 because these numbers having 0 , 5 , 0 , 5 , 0 , 5 unit digit respectively

**Question 4**

**Which of the following numbers are divisible by 9 ?**

**36, 90, 157, 243, 514, 810, 719, 936**

Sol :

⇒A number is divisible by 9 if the sum of its digits is divisible by 9 .

⇒So , the answers are

⇒36 = 3 + 6 = 9 ÷ 9 (which is divisible by 3 and leaves no remainder)

⇒90 = 9 + 0 = 9 ÷ 9 ÷ 9 (which is divisible by 3 and leaves no remainder)

⇒243 = 2 + 4 + 3 = 9 ÷ 9 (which is divisible by 3 and leaves no remainder)

⇒810 = 8 + 1 + 0 = 9 ÷ 9 (which is divisible by 3 and leaves no remainder)

⇒936 = 9 + 3 + 6 = 18 ÷ 9 (which is divisible by 3 and leaves no remainder)

**Question 5**

**Which of the following numbers are divisible by 10 ?**

**75, 80, 140, 400, 670, 895, 985, 990**

Sol :

⇒A number is divisible by 10 if its unit digit is 0

⇒So , the answer is 80 , 140 , 400 , 670 , 990 because all these number having 0 as their unit digit