Question

find the largest number that divides 2623 and 2011 and leaves remainders 5 and 9

Answer 1

2011–9 = 2002

2623–5 = 2618.

Factors of

2002 = 2 x7x11x13

2618 = 2x7x11x17

The HCF = 2 x7x11 = 154.

Check: 2011/154 = quotient = 13, and remainder = 9. Correct.

2623/154 = quotient = 17, and remainder = 5. Correct.

The number is 154.

Answer 2

Hey!!!!!!


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Numbers we'll use

=> 2623 - 5 = 2618

=> 2011 - 9 = 2002

Thus by Prime Factorisation Method,

=> 2618 = 2 x 7 x 11 x 17

=> 2002 = 2 x 11 x 13 x 7

=> HCF(2002,2618) = 2 x 7 x 11

=> HCF = 154

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Hope this helps