Using Euclid's division algorithm,find the la | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Since $1, 2$ and $3$ are the remainders of $1251, 9377$ and $15628$ respectively,we subtract these remainders from the numbers to get numbers that

Vedclass · Accepted Answer

$625$

Vedclass · Answer

(A) Since $1, 2$ and $3$ are the remainders of $1251, 9377$ and $15628$ respectively,we subtract these remainders from the numbers to get numbers that are exactly divisible by the required number.$1251 - 1 = 1250$$9377 - 2 = 9375$$15628 - 3 = 15625$The required number is the $HCF$ of $1250, 9375$ and $15625$.Using Euclid's division algorithm,$a = bq + r$:First,find $HCF$ of $15625$ and $9375$:$15625 = 9375 	imes 1 + 6250$$9375 = 6250 	imes 1 + 3125$$6250 = 3125 	imes 2 + 0$So,$HCF(15625, 9375) = 3125$.Now,find $HCF$ of $3125$ and $1250$:$3125 = 1250 	imes 2 + 625$$1250 = 625 	imes 2 + 0$So,$HCF(3125, 1250) = 625$.Thus,the largest number that divides $1251, 9377$ and $15628$ leaving remainders $1, 2$ and $3$ respectively is $625$.

Using Euclid's division algorithm,find the largest number that divides $1251, 9377$ and $15628$ leaving remainders $1, 2$ and $3$,respectively.

Similar Questions

Prove that $\sqrt{3}+\sqrt{5}$ is irrational.

Prove that $\sqrt{3}$ is an irrational number.

Find the largest number which divides $245$ and $1029$ leaving remainder $5$ in each case.

$\frac{47}{500}$ has $\ldots$ digits after the decimal point in its terminating decimal expansion.

Simplify: $\frac{1}{\sqrt{12-\sqrt{140}}}-\frac{1}{\sqrt{8-\sqrt{60}}}-\frac{2}{\sqrt{10+\sqrt{84}}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module