Question

Which greatest number will divide $3026$ and $5053$ leaving remainders $11$ and $13$ respectively?

• A. $15$
• B. $30$
• C. $45$
• D. $60$

Answer 1

The correct option is C $45$

To find required number we have to find HCF of $(3026-11)$ and $(5053-13)$

Now, HCF of $3015$ and $5040$

To find HCF, we break the given numbers in their prime Factors.

$3015=3\times 3\times 5\times 67$

$5040=2\times 2\times 2\times 2\times 3\times 3\times 5\times 7$

We take common multiples in these two given numbers to get required HCF.

And Common multiples are: $3\times 3\times 5$

So, Required HCF = $45.$

$\therefore$ The required number is $45$.