Question

find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively factorization method​

Answer 1

first we subtract the remainder from the the given numbers and then calculate the the HCF of New numbers .

$solution \: --- >$

given numbers are 285 and 1249 reminders are 9and 7 respectively.

the new numbers after subtracting remainders from their respective numbers are :-

$285 - 9 = 276 \\ 1249 - 7 = 1242$

the required number is their HCF of 276 and 1242

HCF by prime factorization method :-

prime factorization of 1242 =

$2 \times 3 \times 3 \times 3 \times 23 \\ = {2}^{1} \times {3}^{3} \times {23}^{1}$

prime factorization of 276 =

$2 \times 2 \times 3 \times 23 \\ = {2}^{2} \times {3}^{1} \times {23}^{1}$

therefore HCF of two numbers is equal to

$2 \times 3 \times 23$

$= 138$

HCF of 276 and 1242 is 138 .

Hence , the required greatest number which divides 285 and 1249 leaving remainder as 9 and 7 is 138.

hope this answer helped you .