Question

use fundamental theorem of arthmrtics to find the largest integer that divides 449,576,703 leaving remainder 8,9,10 respectively​

Answer 1

Answer:

since the number when divides 449, 576 and 703 leaves remainders 8,9 and 10 respectively,the number must divide (449-8),(576-9) and (703-10)

i.e. 441,567 and 693.

now the largest number that divides 441, 567 and 693 is the HCF of these numbers

441 = 3*3*7*7

567 = 3*3*3*3*7

693 = 3*3*7*11

HCF = 3*3*7

= 63 ans