Question

find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively {by division method} Explain it :)​

Answer 1

Aɴꜱᴡᴇʀ

the greatest number is 1

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Gɪᴠᴇɴ

numbers = 2011 and 2623

and if it was divided with a number then it leaves a remainder of 9 and 5

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Tᴏ ꜰɪɴᴅ

the greatest number that divides 2011 and 2623 and leave a remainder of 9 and 5

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Fᴏʀᴍᴜʟᴀ Uꜱᴇᴅ

A=B(Q)+ R(Euclid's division algorithm)

Where A =Dividend

B=Divisor

Q=Quotient

R= Remainder

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Sᴛᴇᴘꜱ

• If we have to find the greates number then we have to Find their HCF

• but it's given that they leave a remainder so if we subtract the remainder from these numbers then they will be exactly divisible so

2011-9=2002

2623 - 5 =2618

So now let's find their HCF

$2623 \: = 2002(1) + 621 \\ 2002 = 621(3) + 139 \\ 621 \: = 139(4) + 65 \\ 139 = 65(2) + 9 \\ 65 = 9(7) + 2 \\ 9 = 2(4) + 1 \\ 2 = 1(2) + 0$

Thus the gereatest number is

$\large{=1}$

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$\huge{\mathfrak{\blue{Hope\:it\:helps!}}}$