Question

find the sum of integers divisible by 6 between 240 and 340​

Answer 1

Step-by-step explanation:

This problem is best solved using arithmetic progressions.

To find out numbers divisible by 5 between 200 & 800, we consider the AP

205, 210, 215, ... 795

To find the number of terms in this AP,

Use the formula

A + (n-1)d = L

Where,

A is the first term

N is the total number of terms

D is the difference between two terms

L is the last term

On solving it, we get n = 119

Similarly, we make the AP

203, 210, 217, ... 798

Here, n = 86

We have counted the numbers divisible by 5 and 7, but, all those numbers that are divisible by 35 ( being the LCM of 5 and 7), have been counted twice.

So, we come up with an AP of numbers between 200 & 800 that are divisible by 35

AP will be 210,245...770

This AP has 17 terms.

So, finally we have our answer

119 + 86 - 17

= 188.

Answer 2

Answer:

240 ÷ 6 = 40 + 0;

So, 240 = 40 × 6;

So, 240 is divisible by 6;

6 is called a divisor of 240

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Notice that dividing our numbers leaves a remainder:

340 ÷ 6 = 56 + 4;

There is no integer 'n' such that 340 = 'n' × 6.

340 is not divisible by 6;