There are many four-digit positive integers in which the product of the digits is equal to 6!. What is the sum of the largest and smallest such four-digit numbers?
2589 , 2598 , 2859 , 2895 , 2958 , 2985 , 3568 , 3586 , 3658 , 3685 , 3856 , 3865 , 4459 , 4495 , 4549 , 4566 , 4594 , 4656 , 4665 , 4945 , 4954 , 5289 , 5298 , 5368 , 5386 , 5449 , 5466 , 5494 , 5638 , 5646 , 5664 , 5683 , 5829 , 5836 , 5863 , 5892 , 5928 , 5944 , 5982 , 6358 , 6385 , 6456 , 6465 , 6538 , 6546 , 6564 , 6583 , 6645 , 6654 , 6835 , 6853 , 8259 , 8295 , 8356 , 8365 , 8529 , 8536 , 8563 , 8592 , 8635 , 8653 , 8925 , 8952 , 9258 , 9285 , 9445 , 9454 , 9528 , 9544 , 9582 , 9825 , 9852 , Total = 72
The first is the SMALLEST and the last is the LARGEST.
2589 , 2598 , 2859 , 2895 , 2958 , 2985 , 3568 , 3586 , 3658 , 3685 , 3856 , 3865 , 4459 , 4495 , 4549 , 4566 , 4594 , 4656 , 4665 , 4945 , 4954 , 5289 , 5298 , 5368 , 5386 , 5449 , 5466 , 5494 , 5638 , 5646 , 5664 , 5683 , 5829 , 5836 , 5863 , 5892 , 5928 , 5944 , 5982 , 6358 , 6385 , 6456 , 6465 , 6538 , 6546 , 6564 , 6583 , 6645 , 6654 , 6835 , 6853 , 8259 , 8295 , 8356 , 8365 , 8529 , 8536 , 8563 , 8592 , 8635 , 8653 , 8925 , 8952 , 9258 , 9285 , 9445 , 9454 , 9528 , 9544 , 9582 , 9825 , 9852 , Total = 72
The first is the SMALLEST and the last is the LARGEST.
