Question

can anyone explain me about finding a HCF using long division meathod
points to remember while answereing
1-in need an example and you should solve it in anwere only
2- i need breif discripsion
3-i need a leandhy anwere
people who give correct anwere by following all the points,i will mark them as brainlis

Answer 1

H.C.F. by Long Division Method

To find the H.C.F. of the given number we will follow the following steps:

1. We divide the bigger number by smaller one.
2. Divide smaller number in step 1 with remainder obtained in step 1.
3. Divide divisor of second step with remainder obtained in step 2.
4. We will continue this process till we get remainder zero and divisor obtained in end is the required H.C.F

Let’s take few examples for this:

Example 1: Find the H.C.F. of 248 and 492?

To find the solution we will follow the following method i.e. we divide bigger number 492 by smaller one i.e. 248

So the divisor in the end was 4 so the H.C.F of the given numbers is 4

Example 2: Find the H.C.F. of 420 and 396?

To find the solution we will follow the following method i.e. we divide bigger number 420 by smaller one i.e. 396

So the divisor in the end was 12 so the H.C.F of the given numbers is 12

Some points to remember

• – If H is the HCF of two numbers A and B, then H is also a factor of AX and BY, where X and Y are integers. In other words, H is also a factor of multiples of these numbers.
• – If HCF (A,B) is H, then H is also the HCF of (A) and (A+B)
• – If HCF (A,B) is H, then H is also the HCF of (A) and (A-B)
• – If HCF (A,B) is H, then H is also the HCF of (A+B) and (A-B)
• – If HCF=LCM for two numbers, then the numbers must be equal to each other.
• – HCF of two or more fractions is given by:
• (HCF of numerators of all the fractions) / (LCM of denominator of all the fractions)

Answer 2

Step-by-step explanation:

➡️ʜ.ᴄ.ғ. ʙʏ ʟᴏɴɢ ᴅɪᴠɪsɪᴏɴ ᴍᴇᴛʜᴏᴅ

ᴛᴏ ғɪɴᴅ ᴛʜᴇ ʜ.ᴄ.ғ. ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀ ᴡᴇ ᴡɪʟʟ ғᴏʟʟᴏᴡ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ sᴛᴇᴘs:

➡️ᴡᴇ ᴅɪᴠɪᴅᴇ ᴛʜᴇ ʙɪɢɢᴇʀ ɴᴜᴍʙᴇʀ ʙʏ sᴍᴀʟʟᴇʀ ᴏɴᴇ.

➡️ᴅɪᴠɪᴅᴇ sᴍᴀʟʟᴇʀ ɴᴜᴍʙᴇʀ ɪɴ sᴛᴇᴘ 1 ᴡɪᴛʜ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ɪɴ sᴛᴇᴘ 1.

➡️ᴅɪᴠɪᴅᴇ ᴅɪᴠɪsᴏʀ ᴏғ sᴇᴄᴏɴᴅ sᴛᴇᴘ ᴡɪᴛʜ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ʜ.ᴄ.ғ. ʙʏ ʟᴏɴɢ ᴅɪᴠɪsɪᴏɴ ᴍᴇᴛʜᴏᴅ

ᴛᴏ ғɪɴᴅ ᴛʜᴇ ʜ.ᴄ.ғ. ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀ ᴡᴇ ᴡɪʟʟ ғᴏʟʟᴏᴡ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ sᴛᴇᴘs:

➡️ᴡᴇ ᴅɪᴠɪᴅᴇ ᴛʜᴇ ʙɪɢɢᴇʀ ɴᴜᴍʙᴇʀ ʙʏ sᴍᴀʟʟᴇʀ ᴏɴᴇ.

➡️ᴅɪᴠɪᴅᴇ sᴍᴀʟʟᴇʀ ɴᴜᴍʙᴇʀ ɪɴ sᴛᴇᴘ 1 ᴡɪᴛʜ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ɪɴ sᴛᴇᴘ 1.

➡️ᴅɪᴠɪᴅᴇ ᴅɪᴠɪsᴏʀ ᴏғ sᴇᴄᴏɴᴅ sᴛᴇᴘ ᴡɪᴛʜ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ɪɴ sᴛᴇᴘ 2.

➡️ᴡᴇ ᴡɪʟʟ ᴄᴏɴᴛɪɴᴜᴇ ᴛʜɪs ᴘʀᴏᴄᴇss ᴛɪʟʟ ᴡᴇ ɢᴇᴛ ʀᴇᴍᴀɪɴᴅᴇʀ ᴢᴇʀᴏ ᴀɴᴅ ᴅɪᴠɪsᴏʀ ᴏʙᴛᴀɪɴᴇᴅ ɪɴ ᴇɴᴅ ɪs ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ ʜ.ᴄ.ғ.

➡️ʟᴇᴛ’s ᴛᴀᴋᴇ ғᴇᴡ ᴇxᴀᴍᴘʟᴇs ғᴏʀ ᴛʜɪs:

ᴇxᴀᴍᴘʟᴇ 1: ғɪɴᴅ ᴛʜᴇ ʜ.ᴄ.ғ. ᴏғ 248 ᴀɴᴅ 492?

ᴛᴏ ғɪɴᴅ ᴛʜᴇ sᴏʟᴜᴛɪᴏɴ ᴡᴇ ᴡɪʟʟ ғᴏʟʟᴏᴡ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ ᴍᴇᴛʜᴏᴅ ɪ.ᴇ. ᴡᴇ ᴅɪᴠɪᴅᴇ ʙɪɢɢᴇʀ ɴᴜᴍʙᴇʀ 492 ʙʏ sᴍᴀʟʟᴇʀ ᴏɴᴇ ɪ.ᴇ. 248

sᴏ ᴛʜᴇ ᴅɪᴠɪsᴏʀ ɪɴ ᴛʜᴇ ᴇɴᴅ ᴡᴀs 4 sᴏ ᴛʜᴇ ʜ.ᴄ.ғ ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀs ɪs 4

➡️sᴏᴍᴇ ᴘᴏɪɴᴛs ᴛᴏ ʀᴇᴍᴇᴍʙᴇʀ

– ɪғ ʜ ɪs ᴛʜᴇ ʜᴄғ ᴏғ ᴛᴡᴏ ɴᴜᴍʙᴇʀs ᴀ ᴀɴᴅ ʙ, ᴛʜᴇɴ ʜ ɪs ᴀʟsᴏ ᴀ ғᴀᴄᴛᴏʀ ᴏғ ᴀx ᴀɴᴅ ʙʏ, ᴡʜᴇʀᴇ x ᴀɴᴅ ʏ ᴀʀᴇ ɪɴᴛᴇɢᴇʀs. ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ʜ ɪs ᴀʟsᴏ ᴀ ғᴀᴄᴛᴏʀ ᴏғ ᴍᴜʟᴛɪᴘʟᴇs ᴏғ ᴛʜᴇsᴇ ɴᴜᴍʙᴇʀs.

– ɪғ ʜᴄғ (ᴀ,ʙ) ɪs ʜ, ᴛʜᴇɴ ʜ ɪs ᴀʟsᴏ ᴛʜᴇ ʜᴄғ ᴏғ (ᴀ) ᴀɴᴅ (ᴀ+ʙ)

– ɪғ ʜᴄғ (ᴀ,ʙ) ɪs ʜ, ᴛʜᴇɴ ʜ ɪs ᴀʟsᴏ ᴛʜᴇ ʜᴄғ ᴏғ (ᴀ) ᴀɴᴅ (ᴀ-ʙ)

– ɪғ ʜᴄғ (ᴀ,ʙ) ɪs ʜ, ᴛʜᴇɴ ʜ ɪs ᴀʟsᴏ ᴛʜᴇ ʜᴄғ ᴏғ (ᴀ+ʙ) ᴀɴᴅ (ᴀ-ʙ)

– ɪғ ʜᴄғ=ʟᴄᴍ ғᴏʀ ᴛᴡᴏ ɴᴜᴍʙᴇʀs, ᴛʜᴇɴ ᴛʜᴇ ɴᴜᴍʙᴇʀs ᴍᴜsᴛ ʙᴇ ᴇǫᴜᴀʟ ᴛᴏ ᴇᴀᴄʜ ᴏᴛʜᴇʀ.

– ʜᴄғ ᴏғ ᴛᴡᴏ ᴏʀ ᴍᴏʀᴇ ғʀᴀᴄᴛɪᴏɴs ɪs ɢɪᴠᴇɴ ʙʏ:

(ʜᴄғ ᴏғ ɴᴜᴍᴇʀᴀᴛᴏʀs ᴏғ ᴀʟʟ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴs) / (ʟᴄᴍ ᴏғ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ᴏғ ᴀʟʟ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴs)