Let's get this math done. We have 677 and we're going to multiply it by 77. This is the same as taking 677 and adding it to itself 77 times.
Step 1: 0 + 677 = 677
Step 2: 677 + 677 = 1354
Step 3: 1354 + 677 = 2031
Step 4: 2031 + 677 = 2708
Step 5: 2708 + 677 = 3385
Step 6: 3385 + 677 = 4062
Step 7: 4062 + 677 = 4739
Step 8: 4739 + 677 = 5416
Step 9: 5416 + 677 = 6093
Step 10: 6093 + 677 = 6770
Step 11: 6770 + 677 = 7447
Step 12: 7447 + 677 = 8124
Step 13: 8124 + 677 = 8801
Step 14: 8801 + 677 = 9478
Step 15: 9478 + 677 = 10155
Step 16: 10155 + 677 = 10832
Step 17: 10832 + 677 = 11509
Step 18: 11509 + 677 = 12186
Step 19: 12186 + 677 = 12863
Step 20: 12863 + 677 = 13540
Step 21: 13540 + 677 = 14217
Step 22: 14217 + 677 = 14894
Step 23: 14894 + 677 = 15571
Step 24: 15571 + 677 = 16248
Step 25: 16248 + 677 = 16925
Step 26: 16925 + 677 = 17602
Step 27: 17602 + 677 = 18279
Step 28: 18279 + 677 = 18956
Step 29: 18956 + 677 = 19633
Step 30: 19633 + 677 = 20310
Step 31: 20310 + 677 = 20987
Step 32: 20987 + 677 = 21664
Step 33: 21664 + 677 = 22341
Step 34: 22341 + 677 = 23018
Step 35: 23018 + 677 = 23695
Step 36: 23695 + 677 = 24372
Step 37: 24372 + 677 = 25049
Step 38: 25049 + 677 = 25726
Step 39: 25726 + 677 = 26403
Step 40: 26403 + 677 = 27080
Step 41: 27080 + 677 = 27757
Step 42: 27757 + 677 = 28434
Step 43: 28434 + 677 = 29111
Step 44: 29111 + 677 = 29788
Step 45: 29788 + 677 = 30465
Step 46: 30465 + 677 = 31142
Step 47: 31142 + 677 = 31819
Step 48: 31819 + 677 = 32496
Step 49: 32496 + 677 = 33173
Step 50: 33173 + 677 = 33850
Step 51: 33850 + 677 = 34527
Step 52: 34527 + 677 = 35204
Step 53: 35204 + 677 = 35881
Step 54: 35881 + 677 = 36558
Step 55: 36558 + 677 = 37235
Step 56: 37235 + 677 = 37912
Step 57: 37912 + 677 = 38589
Step 58: 38589 + 677 = 39266
Step 59: 39266 + 677 = 39943
Step 60: 39943 + 677 = 40620
Step 61: 40620 + 677 = 41297
Step 62: 41297 + 677 = 41974
Step 63: 41974 + 677 = 42651
Step 64: 42651 + 677 = 43328
Step 65: 43328 + 677 = 44005
Step 66: 44005 + 677 = 44682
Step 67: 44682 + 677 = 45359
Step 68: 45359 + 677 = 46036
Step 69: 46036 + 677 = 46713
Step 70: 46713 + 677 = 47390
Step 71: 47390 + 677 = 48067
Step 72: 48067 + 677 = 48744
Step 73: 48744 + 677 = 49421
Step 74: 49421 + 677 = 50098
Step 75: 50098 + 677 = 50775
Step 76: 50775 + 677 = 51452
Step 77: 51452 + 677 = 52129

So, 677*77 = 52129