Find the largest number which divides 245 and | vedclass

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Question

(C) To find the largest number that divides $245$ and $1029$ leaving a remainder of $5$ in each case,we first subtract the remainder from both numbers

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) To find the largest number that divides $245$ and $1029$ leaving a remainder of $5$ in each case,we first subtract the remainder from both numbers:$245 - 5 = 240$$1029 - 5 = 1024$Now,we need to find the Highest Common Factor $(HCF)$ of $240$ and $1024$.Prime factorization of $240 = 2^4 	imes 3 	imes 5$Prime factorization of $1024 = 2^{10}$The $HCF$ is the product of the lowest power of common prime factors:$HCF(240, 1024) = 2^4 = 16$.Therefore,the largest number is $16$.

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

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