Question

how many natural numbers between 123 and 248 are completely divisble by 5
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Answer 1

Total numbers are : 25

25

Answer 2

Given,

Set of natural numbers between 123 and 248.

To find,

How many numbers are completely divisible by 5.

Solution,

• If the number is completely divisible by 5 then its once place can only be 0 or 5.

• The first number starting from 123 that is completely divisible by 5 is 125.

• The last number between 123 and 248 that is completely divisible by 5  from the ending is 245.

• So we get the series as:

           125,130,135,140...245

• These are the numbers between 123 and 248 that are completely divisible by 5.

• This series is an Arithmetic Progression with a common difference(d) as 5.

• The first term a  = 125

• The last term(an) = 245.

• Putting this in the formula of AP:

               an = a + (n-1)d

⇒   245 = 125 + (n-1)5

⇒   245 - 125 = 5n - 5

⇒   120 = 5n - 5

⇒   125 = 5n

⇒   n = 25.

Hence, the number of natural numbers between 123 and 248 that is completely divisible by 5 is 25.