Q. 14.8( 4 Votes )

# What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

A. 15

B. 16

C. 9

D. 5

Answer :

We know that Dividend = Divisor × Quotient + Remainder

According to the problem :

Dividend 1 = 245

Dividend 2 = 1029

Dividend - Remainder = Divisor × Quotient

So Dividend 1- Remainder = 240 = Divisor × Quotient 1

Prime Factor of 240 = 2^{4} × 3 × 5

Dividend 2 – Remainder = 1024 = Divisor × Quotient 2

Prime Factor of 1024 = 2^{4} × 2^{6}

Since, the Divisor is common for both the numbers we need to find the Highest Common Factor between both the numbers. From the Prime factors, we find the

__Highest Common Factor between the two numbers is 2 ^{4} = 16__

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