Question

Find the greatest number which divides 260 , 1314 and 1331 leaves remainder 5 in each case​

Answer 1

$\sf{\underline{Answer:}}$

The greatest number is 17.


$\sf{\underline{Solution:}}$

$\sf{\underline{The\:given\:numbers\:are:}}$

$\boxed{\sf{260,\:1314\:and\:1331}}$

$\sf{\underline{Now:}}$

To find the greatest number that divides 260, 1314 and 1331 and leaves remainder 5 in each case:

At first, we will subtract 5 from the given numbers.

$\sf{\underline{Then:}}$

We have to find the HCF of the resulting numbers:

$\sf{\underline{In\:order\:to\:obtain\:the\:required\:number.}}$

$\sf{\underline{Now:}}$

$\sf{260 \:-\:5 = \:255}$

$\sf{1314\:-\: 5 = \:1309}$

$\sf{1331\:-\: 5 =\:1326}$

$\sf{\underline{Now:}}$

Prime factorisation of 255, 1309 and 1326:

$\boxed{\sf{255 = 3 \times 5 \times 17}}$

$\boxed{\sf{1309 = 7 \times 11 \times 17}}$

$\boxed{\sf{1326 = 2 \times 3 \times 13 \times 17}}$

HCF = $\boxed{\sf{17}}$

$\sf{\underline{Hence:}}$

The greatest number that divides 260, 1314 and 1331 and leaves remainder 5 in each case is 17.

Answer 2

Answer:

Step-by-step explanation:

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