Find the largest number that divides 2053 and | vedclass

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

Question

(D) To find the largest number that divides $2053$ and $967$ leaving remainders $5$ and $7$ respectively,we first subtract the remainders from the giv

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(D) To find the largest number that divides $2053$ and $967$ leaving remainders $5$ and $7$ respectively,we first subtract the remainders from the given numbers.$2053 - 5 = 2048$$967 - 7 = 960$Now,we need to find the Highest Common Factor $(HCF)$ of $2048$ and $960$.Using the prime factorization method:$2048 = 2^{11}$$960 = 2^6 	imes 3 	imes 5$The $HCF$ is the product of the lowest powers of common prime factors:$HCF = 2^6 = 64$Therefore,the largest number is $64$.

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

Similar Questions

Find the $g.c.d.$ of $240$ and $6552$ using Euclid's division algorithm.

$LCM(15, 21, 35) = .........$

Prove that the following number is irrational: $\sqrt{11}$

The smallest positive number greater than $5$ such that when it is divided by $20, 30,$ or $40,$ it leaves the remainder $5$ is:

State whether the following rational number has a terminating decimal expansion or not. If it has,then find it: $\frac{9}{30}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module