Question

What remainder does the sum 2222+2333 leave after division? Each one has an answer! Need answer quickly! 18 points!

by 4?

by 6?

by 9?

by 12?

Answer 1

• Dividing by 4

2222 = 2220 + 2 = 555 * 4 + 2

2333 = 2332 + 1 = 583 * 4 + 1

Then

2222 + 2333 = (555 + 583) * 4 + 3

leaving a remainder of 3.

• Dividing by 6

2222 = 2220 + 2 = 370 * 6 + 2

2333 = 2328 + 5 = 388 * 6 + 5

Then

2222 + 2333 = (370 + 388) * 6 + 7 = (370 + 388 + 1) * 6 + 1

leaving a remainder of 1.

• Dividing by 9

2222 = 2223 - 1 = 741 * 3 - 1

2333 = 388 * 6 + 5 = (388 * 2) * 3 + 5 = (388 * 2 + 1) * 3 + 2

Then

2222 + 2333 = (741 + 388 * 2 + 1) * 3 + 1

leaving a remainder of 1.

• Dividing by 12

2222 = 555 * 4 + 2 = 185 * 3 * 4 + 2 = 185 * 12 + 2

2333 = 2400 - 67 = 2400 - 60 - 7 = (200 - 5) * 12 - 7

Then

2222 + 2333 = (185 + 200 - 5) * 12 - 5

leaving a remainder of -5, or 7. (because 12 - 5 = 7)