Question

Find the largest number which divides 630 and 940 leaving remainder 6 and 4 respectively

Answer 1

simple method:
numbers which divide by 630 leaving remainder of 6:
636 1266 1896 2526 3156 3786 4416 ...

numbers which divide by 940 leaving remainder of 4:
944 1884 2824 3764 ...... looks hopeless

alternate method

Let that number be k
then
k/630 = x + 6/630 --> k = 630x + 6
k/940 = y + 4/940 --> k = 940y + 4
where both x and y are whole numbers

630x + 6 = 940y + 4
630x - 940y = -2
315x - 470y = -1
470y - 315x = 1
5(94x - 63y) = 1
no way!, the left side is a multiple of 5, and x and y are whole numbers. That left side can never be 1

no such number

Answer 2

Ccgczvzgga@6178182(

Answer 3

Try 12. 630/12=52 R6 and 940/12=78 R4 but is 12 the largest number possible?

Answer 4

Xkvwkvucsu

Answer 5

Amazing!😄👏