Question

find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively in each case

Answer 1

The formula =>

Dividend = ( Divisor × Quotient ) + Remainder

Dividend in first place = 2011 , remainder = 9

2011 = ( Divisor × Quotient ) + 9

Divisor × Quotient = 2011 - 9 = 2002

Now, list out the factors

2 × 7 × 11 × 13

The second dividend

Apply the same formula

we get,

Divisor × Quotient = 2618

List out the factors

2 × 7 × 11 × 17

HCF is 2 × 7 × 11

HCF is 154

Divisor is 154

Now, the first one

Divisor × Quotient = 2002

154 × Quotient = 2002

Quotient = 2002/154

Quotient = 13

The second one

Divisor × Quotient = 2618

154 × Quotient = 2618

Quotient = 17

First one , and second one

Dividend = 2011 , 2623

Divisor = 154 , 154

Remainder = 9 , 5

Quotient = 13 , 17