We have Master and Slave Replication running since 2 year and today we found slave disk if full and mysql process is dead (because disk is full and not able to start back). I have found we have tons of bin file on Master

mysql> show binary logs;
+------------------+------------+
| Log_name         | File_size  |
+------------------+------------+
| mysql-bin.000001 |        673 |
| mysql-bin.000002 |       1511 |
| mysql-bin.000003 |  314113849 |
| mysql-bin.000004 |   73402521 |
| mysql-bin.000005 |        125 |
| mysql-bin.000006 |       5681 |
| mysql-bin.000007 |        125 |
| mysql-bin.000008 |       1529 |
| mysql-bin.000009 |  772739549 |
| mysql-bin.000010 |      40635 |
| mysql-bin.000011 |   16928499 |
| mysql-bin.000012 |     159269 |
| mysql-bin.000013 |       9481 |
| mysql-bin.000014 |      58169 |
| mysql-bin.000015 |  301881886 |
| mysql-bin.000016 |        217 |
| mysql-bin.000017 |        217 |
| mysql-bin.000018 |       3533 |
| mysql-bin.000019 |  323644264 |
| mysql-bin.000020 | 1073741894 |
| mysql-bin.000021 | 1073741962 |
| mysql-bin.000022 | 1073742126 |
| mysql-bin.000023 | 1073742901 |
| mysql-bin.000024 | 1073742080 |
| mysql-bin.000025 | 1073742064 |
| 
|...output..omitted..
|
| mysql-bin.000120 | 1073742253 |
| mysql-bin.000121 | 1073742378 |
| mysql-bin.000122 | 1073741927 |
| mysql-bin.000123 | 1073743016 |
| mysql-bin.000124 |  478325517 |
+------------------+------------+
124 rows in set (0.01 sec)

Question:

1. is it safe to delete bin file on master and try re-sync?
2. or should i remove bin file on slave and try to bring back slave machine back?
3. what would be the best step to bring back slave in working condition?