Question

what is the number between 800 and 900 which is exactly divisible by 13 and 17​

Answer 1

$\large\bf{\underline\green{☕︎Good \: Morning☕︎}}$

First let us divide the number 300 by 17.

We get,

300/17 = 17 x 17 + 11

Since the remainder is 11, the next multiple of 17 would be (300 +6) = 306

306 = 17 x 18

Now dividing 900 by 17 we get,

900/17 = 17 x 52 + 16

Since the remainder is 16 only 1 needs to be added to 900 to get the next multiple.

So 901 is a multiple of 17.

But we need numbers between 300 and 900. So the previous multiple is

901 - 17 = 884

884 = 17 X 52

Since the first 18th multiple is above 300, that means we can ignore the previous 17 multiples of 17.

So,

52 - 17 = 35

There are 35 numbers lying between 300 and 900 that are divisible by 17.

Answer 2

Sᴏʟᴜᴛɪᴏɴ:

Sᴛᴇᴘ 1 - ʟᴄᴍ ᴏғ 13 ᴀɴᴅ 17 ; 13 × 17 = 221

Sᴛᴇᴘ 2 - Sᴏ ᴛʜᴇ ᴍᴜʟᴛɪᴘʟᴇ ᴏғ 221 ʙᴇᴛᴡᴇᴇɴ 800 ᴀɴᴅ 900 ᴡɪʟʟ ʙᴇ ᴅɪᴠɪsɪʙʟᴇ ʙʏ 13 ᴀɴᴅ 17 .

Sᴛᴇᴘ 3 - Wʜᴇɴ ᴡᴇ ᴅɪᴠɪᴅᴇ ʟᴏᴡᴇsᴛ ɴᴜᴍʙᴇʀ 800 ʙʏ 221.

Sᴛᴇᴘ 4 - Nᴏᴡ ʀᴇᴍɪɴᴅᴇʀ = 137.

Sᴛᴇᴘ 5 - Nᴏᴡ ᴡᴇ sᴜʙᴛʀᴀᴄᴛ ғʀᴏᴍ Lᴄᴍ ᴛᴏ ʀᴇᴍɪɴᴅᴇʀ = 221 - 137 = 84.

Sᴛᴇᴘ 6 - Nᴏᴡ ʀᴇǫᴜɪʀᴇᴅ ɴᴜᴍʙᴇʀ = (ʟᴏᴡᴇsᴛ ɴᴜᴍʙᴇʀ ± Sᴜʙᴛʀᴀᴄᴛ ɴᴜᴍʙᴇʀ)

800 ± 84 = 884

(Tʜɪs ɴᴜᴍʙᴇʀ ɪs ᴅɪᴠɪᴅᴇᴅ ʙʏ ʙᴏᴛʜ 13 ᴀɴᴅ 17)

Hᴏᴘ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ ❤️