226186081502
Let k be the whole number we are searching for.
Let 823519 divided by k be n, remainder 3r
and 274658 divided by k be m, remainder r
Then
823519 = n k + 3r and
274658 = m k + r
Multiply the second equation by three and subtract the first:
455 = (3m - n) k
So k is a factor of 455.
That means it is 1,5,7,13,35,65,91 or 455
I can write 823519 as 1809*455 + 424
Each time I divide this by one of the eight possibilities for k the 1809*455 part will
go exactly and not change the remainder. so I only need to look at the 424 part.
Listing the possibilities:
424 divided by 1 has a remainder of 0
424 divided by 5 has a remainder of 4
424 divided by 7 has a remainder of 4
424 divided by 13 has a remainder of 8
424 divided by 35 has a remainder of 179
424 divided by 65 has a remainder of 34
424 divided by 91 has a remainder of 60
424 divided by 455 has a remainder of 424
The 1 and 91 choices are the only ones which leave a remainder which is a multiple of 3
274658 divided by 91 has a remainder of 20.
Therefore the answer is 91!
A subtle point is that the remainder is always a positive number. So -7 divided by 3 is -3, remainder 2 (rather than -2, remainder -1). This is important for the date of Easter because we must often calculate the remainder when dividing into a negative number. Since in that case we are not interested in the quotient it is sufficient to calculate the negative remainder and then simply add to it the number we were dividing by. So -11 mod 3 may be calculated as: -11 divided by 3 is -3, remainder -2, so the number required is -2 + 3 = 1.
2519
85. A number when divided by 238, leaves a remainder 79. What will be the remainder when the number is divided bv 17 ? (1) 8 (2) 9 (3) 10 @) 11
43 divided by 11 is 3 with remainder 10.
79 divided by 8 is 9 with remainder 7.
226186081502
402.4286
0.1613
Dividing by 3 and then by 5 is equivalent to to dividing by 15; therefore, the remainder will be the same.
Dividing 45 by 7 results in the answer 6... with a remainder of 3.
Dividing 37 by 5 gives 7.4 or 7 remainder 2.
3,796 divided by 48 is 79 with remainder 4.
506
the Remainder is divided by the outside number to form another decimal, which is added onto the end of the answer.
0.2286
The largest remainder when dividing by 6 is 5. This is true because if the remainder is 6, the 6 would divide into the number again. For example: 35 divided by 6 is 5 remainder 5. 36 divided by 6 cannot be 5 remainder 6 because 6 will divide into 36 again. The answer would be 6.
You can't divide something as a remainder, you must forst put it into decimal form. You can do this by dividing two by whatever the number you divided by in the equation that resulted in the answer '19 remainder 2.'