Question

how many numbers from 29 to 79 are exactly divisible by 11

Answer 1

Five numbers from 29 to 79 are exactly divisible by 11.

They are 33, 44, 55, 66 and 77.

Answer 2

Total numbers are 5 from 29 to 79; which are divisible by 11.

Given:

• Numbers from 29 to 79.

To find:

• How many numbers are exactly divisible by 11.

Solution:

Formula to be used:

General term of an A.P.

$\boxed{\bf a_n = a + (n - 1)d }$

where,

a: first term

d: common difference

Step 1:

Write the first number and last number.

We know that,

After 29, 33 is divisible by 11.

So,

$\bf a = 33$

Last term is 77, before 79; which is divisible by 11.

Let nth term is $\bf a_n = 77$

Common difference in consecutive multiples of 11 is 11, thus

Common difference d= 11

Step 2:

Find the total numbers.

Put the values in the general term, to find the value of n; i.e. total numbers

$77 = 33 + (n - 1)11$

$77 - 33 = 11(n - 1)$

$44 = 11(n - 1)$

$n - 1 = \frac{44}{11}$

$n - 1 = 4$

$\bf n = 5$

Thus,

Total numbers are 5 from 29 to 79; which are divisible by 11.

Learn more:

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2) Find the sum of all 3 digit natural multiples of 6.

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