Divisibility

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create a three-digit number. Try to create a three-digit number divisible by the greatest (or fewest) amount of the following factors: 2, 3, 4, 5, 6, 8, 9 or 10.

Hint

What number should the final digit be such that it is divisible by 2, 5 and 10?

What should the three digits add up to so that it is divisible by 3 and 9?

What should the middle digit be so that it is divisible by 4?

Answer

Greatest number of factors:  360 and 720 are both divisible by 2,3,4,5,6,8,9 and 10.
Fewest number of factors:  any three digit prime with unique digits would have none of the given numbers as factors. There are more than 20 such numbers (e.g. 103, 347, 521, 849).

Source: Kelly Zinck

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20 comments

  1. I believe the answer drop down box is wrong as 360 and 740 are divisible by 2, 3, 4, 5, 6, 8, 9, and 10. The six is missing form the drop down menu answer. Thanks for the cool problem.

  2. Never Telling My Name

    you should put 180 in “2, 3, 4, 5, 6, 8, 9”

  3. 360- can be divided by 2, 3,4,6, 9and 10

  4. 360 has the greatest

  5. The number 360 is divisible by them all.

  6. Karen Mullings

    720

  7. Surbhi JINANDRA

    divisible by all

  8. 360 is the least number divisible by all.

  9. 720

  10. Always a good day to learn something new! 😉

  11. 360 and 720

  12. Rudolf Österreicher

    There are 240 numbers not divisible by 2, 3 or 5 (and therefore not divisible by 4, 6, 8, 9 or 10 either) and not all of them are prime numbers (for example, 133 = 7 * 19):

    101
    103
    107
    109
    113
    119
    121
    127
    131
    133
    137
    139
    143
    149
    151
    157
    161
    163
    167
    169
    173
    179
    181
    187
    191
    193
    197
    199
    203
    209
    211
    217
    221
    223
    227
    229
    233
    239
    241
    247
    251
    253
    257
    259
    263
    269
    271
    277
    281
    283
    287
    289
    293
    299
    301
    307
    311
    313
    317
    319
    323
    329
    331
    337
    341
    343
    347
    349
    353
    359
    361
    367
    371
    373
    377
    379
    383
    389
    391
    397
    401
    403
    407
    409
    413
    419
    421
    427
    431
    433
    437
    439
    443
    449
    451
    457
    461
    463
    467
    469
    473
    479
    481
    487
    491
    493
    497
    499
    503
    509
    511
    517
    521
    523
    527
    529
    533
    539
    541
    547
    551
    553
    557
    559
    563
    569
    571
    577
    581
    583
    587
    589
    593
    599
    601
    607
    611
    613
    617
    619
    623
    629
    631
    637
    641
    643
    647
    649
    653
    659
    661
    667
    671
    673
    677
    679
    683
    689
    691
    697
    701
    703
    707
    709
    713
    719
    721
    727
    731
    733
    737
    739
    743
    749
    751
    757
    761
    763
    767
    769
    773
    779
    781
    787
    791
    793
    797
    799
    803
    809
    811
    817
    821
    823
    827
    829
    833
    839
    841
    847
    851
    853
    857
    859
    863
    869
    871
    877
    881
    883
    887
    889
    893
    899
    901
    907
    911
    913
    917
    919
    923
    929
    931
    937
    941
    943
    947
    949
    953
    959
    961
    967
    971
    973
    977
    979
    983
    989
    991
    997

  13. I wonder why 7 is left out and 10 has been included.

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