Question

How many. Natural no. Between 200 to 400 are divided by 4?

Answer 1

The numbers divisible by 8 are also divisible by 4.

The numbers divisible by 10 are also divisible by 5.

First number after 200 that is divisible by 4 is 204. And last one is 396. (Exclusive of 200 and 400)

Total number of terms in the series 204, 208, 212,…..396

Last term= first term +(number of terms-1)*(common difference)

Number of terms= 49;

First number after 200 that is divisible by 5 after 200 is 205 and last one being 395.

Total number of terms between 200 and 400 that are divisible by 5 will be 39;

Now, accounting for common multiples of 4 and 5.

LCM of 4 and 5 is 20;

So first term after 200 that is divisible by 20 will be 220 and last one will be 380.

Total number of terms= 9;

So total number of terms= (Number of terms divisible by 4)+(Number of terms divisible by 5)—( Number of terms divisible by both, i.e, 20)

Total number of terms= 49+39-9= 79;

79 is the answer.

Answer 2

Answer:

The number of natural numbers between 200 and 400 divided by 4 = 49

Step-by-step explanation:

To find,

The number of natural numbers between 200 and 400 divisible by 4.

Recall the formula

The number of terms of the AP = n = $\frac{t_n - t_1}{d} + 1$

tₙ = nth term of the AP

t₁ = first term of the AP

d = common difference of the AP

Solution:

The terms between 200 and 400 divisible by 4 are

204,208,212,..............396

This forms an AP with common difference = d = 4

The first term of the AP = t₁=  204

The last term of the AP = tₙ =  396

The number of natural numbers between 200 and 400 divided by 4 = The number of terms in the AP

$n = \frac{t_n - t_1}{d} + 1$

$n = \frac{396 - 204}{4} + 1$

= $\frac{192}{4} +1$

= 48+1

= 49

The number of natural numbers between 200 and 400 divided by 4 = 49

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