Let's roll up our sleeves and solve this. We have 583 and we're going to multiply it by 13, essentially adding 583 to itself 13 times.
Step 1: 0 + 583 = 583
Step 2: 583 + 583 = 1166
Step 3: 1166 + 583 = 1749
Step 4: 1749 + 583 = 2332
Step 5: 2332 + 583 = 2915
Step 6: 2915 + 583 = 3498
Step 7: 3498 + 583 = 4081
Step 8: 4081 + 583 = 4664
Step 9: 4664 + 583 = 5247
Step 10: 5247 + 583 = 5830
Step 11: 5830 + 583 = 6413
Step 12: 6413 + 583 = 6996
Step 13: 6996 + 583 = 7579

So, 583*13 = 7579