Let's roll up our sleeves and solve this. We have 597 and we're going to multiply it by 17, essentially adding 597 to itself 17 times.
Step 1: 0 + 597 = 597
Step 2: 597 + 597 = 1194
Step 3: 1194 + 597 = 1791
Step 4: 1791 + 597 = 2388
Step 5: 2388 + 597 = 2985
Step 6: 2985 + 597 = 3582
Step 7: 3582 + 597 = 4179
Step 8: 4179 + 597 = 4776
Step 9: 4776 + 597 = 5373
Step 10: 5373 + 597 = 5970
Step 11: 5970 + 597 = 6567
Step 12: 6567 + 597 = 7164
Step 13: 7164 + 597 = 7761
Step 14: 7761 + 597 = 8358
Step 15: 8358 + 597 = 8955
Step 16: 8955 + 597 = 9552
Step 17: 9552 + 597 = 10149

So, 597*17 = 10149