Question

find the greatest no. that will divide 445,572and 699 leaving remainder 4,5 and 6 respectively

Answer 1

Given :-

• Remainers left after dividing 445, 572 & 699 with the greatest possible number = 4, 5 & 6 respectively.

To Find :-

• The required greatest number.

Solution :-

Let's start by subtracting the remainders from their corresponding numbers. We get,

• 445 - 4 = 441
• 572 - 5 = 567
• 699 - 6 = 693

Now, these resulting numbers will be completely divisible by our required number.

Therefore, the required number will be the HCF of 441, 567 and 693.

By Prime Factorisation method, we get,

$\begin{tabular}{c|ccc}3&441,&567,&693\\\cline{2-4}3&147,&189,&231\\\cline{2-4}7&49,&63,&77\\\cline{2-4}&7,&9,&11\\\cline{2-4}\end{tabular}$

Hence,

• The required number is = 3 × 3 × 7 = 63.