Question

find the largest +ve integer that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively.

Answer 1

lets assume that the integer we are trying to find is X , X should have upper value (x < z) right ?

Answer 2

i dnt knw

Answer 3

ok lets try X < 1000000

Answer 4

k

Answer 5

believe it or not there isnt any integer that is less than 1000000 that satisfy you conditions
, but if x < 10000000 then x would be 78850175

Answer 6

i didn't get u

Answer 7

there isnt an integer X <1000000 will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively.
but there is integer X < 10000000 that find the largest +ve integer that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively. and it is 78850175

Answer 8

i wrote a simple C++ program to get this values btw

Answer 9

srry i dnt need d solution
i dnt ask u anythng

Answer 10

"398,436 and 542 leaving remainders 7,11 and 15 respectively."
now we know that 398-7, 436-11, 543-15 will be divisible by that highest possible positive integer we are trying to find. (because if you divide a particular number m by n and you left a remainder r then m-r will be divisible by n. tell me if you need a proof of this). And so what we are now trying to find is the largest possible number that will divide 436-11=425, 398-7=391, 543-15=527. Now wait a minute, the greatest possible number that will divide 425, 398 and 527 are their greatest common factor! So now we find the gcf of 425, 398, and 527.
first you break these composite numbers to its prime components.
425=5x5x17
now I don't know what are the prime factors of 391 and 527. now I know that 425, 391, and 527 have a gcf which is not 1. Let's look at 391 and 527. they don't seem to be divisible by 5, hence they could only be divisible by 17. dividing them both by 16 will give you its prime factors:
391=23x17
527=31x17
and so the gcf of 391, 527, and 391 17, hence 17 will be the largest possible positive integer that will divide 398, 436, and 542 and leave a remainder 7, 11, and 15 respectively.
recheck:
398=17x23 + 7
436=17x25 + 11
542=17x31+15