Question

Find the greatest number which divides 645and 792 leaving remainders 7and 9 retrospectively

Answer 1

$\underline{Step \: 1 \: : \: Subtract \: 7 \: and \: 9 \: from \: 645 \: and \: 792}$

645 - 7 = 638

792 - 9 = 783

We obtained two new numbers, 638 and 783


$\underline{Step \: 2 \: : \: Find \: the \: prime \: factors \: of \: the \: new \: numbers}$

638 = 2 × 11 × 29

783 = 3 × 3 × 3 × 29


$\underline{Step \: 3 \: : \: Find \: the \: HCF}$

We have common factors only 29

∴ HCF = 29



∴ $\texttt{The \: greatest \: number \: which \: divides } \\ \texttt{ 645 \: and \: 792 \: leaving \: remainders \: 7} \\ \texttt{ and \: 9 \: respectively \: is}\red{\boxed{\boxed{\blue{29}}}}$

Answer 2

Hello !

Thanks for asking this!

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Solution :

Find the number which is exactly divided by required number for 645

On dividing 645 by it's required number

We get a remainder= 7

⇒ 645 - 7 = 638

The number which is exactly divided by the required number = 638

Find the number which is also exactly divided by required number for 792  

On dividing 792 by it's required number

We get a remainder = 9

⇒ 792 - 9 = 783

The number which is also exactly divided by required number is 783

Find the prime factorisation of 638 and 782 in order to finding a greatest number which divides 645 and 792 leaving remainders 7 and 9 respectively

Prime Factorisation of 638 = 2 * 11 * 29

Prime Factorisation of  783 = 3 * 3 * 3 * 29

HCF of 638 and 782 is 29

Therefore , the required greatest number which divides 645 and 792 leaving a remainder 7 and 9 respectively is 29

#BE BRAINLY

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