Question

Find the greatest number which divides 279 and 435 leaving remainders 7 and 10 respectively

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

279 - 7 = 272

435 - 10 = 425

★Prime factorisation of 272 and 425 :-

272 = 2 × 2 × 2 × 2 × 2 × 17

425 = 5 × 5 × 17

★HCF = 17

•Here we get 17 as greatest number.

Answer 2

Answer :

Required greatest Number = 17.

Step-by-step explanation :

Given that :

Greatest number which divides 279 and 435 leaving remainders 7 and 10 respectively.

To Find :

Find the greatest number.

Solution :

⇒ 279 - 7 = 272.

⇒ 435 - 10 = 425.

Now, Well will find HCF of 272 and 425.

★ 272:

$\begin{array}{r|l} 2 & 272 \\ \cline{1-2} 2 & 136 \\\cline{1-2} 2 & 68 \\\cline{1-2} 2 & 34 \\\cline{1-2} 17& 17 \\\cline{1-2} & 1\end{array}$

★ 435 :

$\begin{array}{r|l} 5 & 435 \\ \cline{1-2} 5 & 85 \\\cline{1-2} 17 & 17 \\\cline{1-2} & 1\end{array}$

Now Factors of both numbers :

272 = 2 × 2 × 2 × 2 × 2 × 17✔️

425 = 5 × 5 × 17✔️

H.C.F of 272 and 435 is 17.

$\bigstar\;\textbf{\underline{\underline{Hence,The required greatest number is 17.}}}$