4 x 100 + 5 x 10 + 6 = 456
_______
53 | 24182
| 21200
_______
| 2982
| 2650
_______
| 332
| 318
_______
| 14

Count of mangoes to distribute = 24182
_______
First we give 4 x 100 mangoes to each of 53 boyes
So, we have taken 21200 manogoes out of all the mangoes = 24182 mangoes
_______
Count of mangoes remaining = 2982 mangoes
Then we give 5 x 10 mangoes to each of 53 boyes
So, we have taken 2650 manogoes out of remaining mangoes = 2982 mangoes
_______
Count of mangoes remaining = 332 mangoes
Then we give 6 mangoes to each of 53 boyes
So, we have taken 318 manogoes out of remaining mangoes = 332 mangoes
_______
Count of mangoes remaining = 14 mangoes