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Ken Ward's Mathematics Pages

Number Theory

See Divisibility for an explanation


Power of 10Mod 2
11
100
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 3
11
101
1001
10001
100001
1000001
10000001
100000001
1000000001
10000000001
100000000001

Power of 10Mod 4
11
102
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 5
11
100
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 6
11
104
1004
10004
100004
1000004
10000004
100000004
1000000004
10000000004
100000000004

Power of 10Mod 7
11
103
1002
10006
100004
1000005
10000001
100000003
1000000002
10000000006
100000000004

Power of 10Mod 8
11
102
1004
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 9
11
101
1001
10001
100001
1000001
10000001
100000001
1000000001
10000000001
100000000001

Power of 10Mod 10
11
100
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 11
11
1010
1001
100010
100001
10000010
10000001
1000000010
1000000001
100000000010
100000000001

Power of 10Mod 12
11
1010
1004
10004
100004
1000004
10000004
100000004
1000000004
10000000004
100000000004

Power of 10Mod 13
11
1010
1009
100012
100003
1000004
10000001
1000000010
1000000009
100000000012
100000000003

Power of 10Mod 14
11
1010
1002
10006
100004
10000012
10000008
1000000010
1000000002
10000000006
100000000004

Power of 10Mod 15
11
1010
10010
100010
1000010
10000010
100000010
1000000010
10000000010
100000000010
1000000000010

Power of 10Mod 16
11
1010
1004
10008
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 17
11
1010
10015
100014
100004
1000006
10000009
100000005
10000000016
10000000007
100000000002

Power of 10Mod 18
11
1010
10010
100010
1000010
10000010
100000010
1000000010
10000000010
100000000010
1000000000010

Power of 10Mod 19
11
1010
1005
100012
100006
1000003
100000011
1000000015
10000000017
100000000018
100000000009

Power of 10Mod 20
11
1010
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 21
11
1010
10016
100013
100004
10000019
10000001
1000000010
10000000016
100000000013
100000000004

Power of 10Mod 22
11
1010
10012
100010
1000012
10000010
100000012
1000000010
10000000012
100000000010
1000000000012

Power of 10Mod 23
11
1010
1008
100011
1000018
10000019
10000006
1000000014
1000000002
100000000020
1000000000016

Power of 10Mod 24
11
1010
1004
100016
1000016
10000016
100000016
1000000016
10000000016
100000000016
1000000000016

Power of 10Mod 25
11
1010
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 26
11
1010
10022
100012
1000016
1000004
100000014
1000000010
10000000022
100000000012
1000000000016

Power of 10Mod 27
11
1010
10019
10001
1000010
10000019
10000001
1000000010
10000000019
10000000001
1000000000010

Power of 10Mod 28
11
1010
10016
100020
100004
10000012
10000008
1000000024
10000000016
100000000020
100000000004

Power of 10Mod 29
11
1010
10013
100014
1000024
1000008
100000022
1000000017
10000000025
100000000018
100000000006

Power of 10Mod 30
11
1010
10010
100010
1000010
10000010
100000010
1000000010
10000000010
100000000010
1000000000010

Power of 10Mod 31
11
1010
1007
10008
1000018
10000025
10000002
1000000020
10000000014
100000000016
100000000005

Power of 10Mod 32
11
1010
1004
10008
1000016
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 33
11
1010
1001
100010
100001
10000010
10000001
1000000010
1000000001
100000000010
100000000001

Power of 10Mod 34
11
1010
10032
100014
100004
1000006
100000026
1000000022
10000000016
100000000024
100000000002

Power of 10Mod 35
11
1010
10030
100020
1000025
1000005
100000015
1000000010
10000000030
100000000020
1000000000025

Power of 10Mod 36
11
1010
10028
100028
1000028
10000028
100000028
1000000028
10000000028
100000000028
1000000000028

Power of 10Mod 37
11
1010
10026
10001
1000010
10000026
10000001
1000000010
10000000026
10000000001
1000000000010

Power of 10Mod 38
11
1010
10024
100012
100006
10000022
100000030
1000000034
10000000036
100000000018
1000000000028

Power of 10Mod 39
11
1010
10022
100025
1000016
1000004
10000001
1000000010
10000000022
100000000025
1000000000016

Power of 10Mod 40
11
1010
10020
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 41
11
1010
10018
100016
1000037
1000001
100000010
1000000018
10000000016
100000000037
100000000001

Power of 10Mod 42
11
1010
10016
100034
100004
10000040
100000022
1000000010
10000000016
100000000034
100000000004

Power of 10Mod 43
11
1010
10014
100011
1000024
10000025
100000035
100000006
10000000017
100000000041
1000000000023

Power of 10Mod 44
11
1010
10012
100032
1000012
10000032
100000012
1000000032
10000000012
100000000032
1000000000012

Power of 10Mod 45
11
1010
10010
100010
1000010
10000010
100000010
1000000010
10000000010
100000000010
1000000000010

Power of 10Mod 46
11
1010
1008
100034
1000018
10000042
10000006
1000000014
1000000002
100000000020
1000000000016

Power of 10Mod 47
11
1010
1006
100013
1000036
10000031
100000028
1000000045
10000000027
100000000035
1000000000021

Power of 10Mod 48
11
1010
1004
100040
1000016
10000016
100000016
1000000016
10000000016
100000000016
1000000000016

Power of 10Mod 49
11
1010
1002
100020
100004
10000040
10000008
1000000031
10000000016
100000000013
1000000000032

Power of 10Mod 50
11
1010
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 51
11
1010
10049
100031
100004
10000040
100000043
1000000022
10000000016
10000000007
1000000000019

Power of 10Mod 52
11
1010
10048
100012
1000016
1000004
100000040
1000000036
10000000048
100000000012
1000000000016

Power of 10Mod 53
11
1010
10047
100046
1000036
10000042
100000049
1000000013
10000000024
100000000028
1000000000015

Power of 10Mod 54
11
1010
10046
100028
1000010
10000046
100000028
1000000010
10000000046
100000000028
1000000000010

Power of 10Mod 55
11
1010
10045
100010
1000045
10000010
100000045
1000000010
10000000045
100000000010
1000000000045

Power of 10Mod 56
11
1010
10044
100048
1000032
10000040
10000008
1000000024
10000000016
100000000048
1000000000032

Power of 10Mod 57
11
1010
10043
100031
1000025
10000022
100000049
1000000034
10000000055
100000000037
1000000000028

Power of 10Mod 58
11
1010
10042
100014
1000024
1000008
100000022
1000000046
10000000054
100000000018
100000000006

Power of 10Mod 59
11
1010
10041
100056
1000029
10000054
10000009
1000000031
10000000015
100000000032
1000000000025

Power of 10Mod 60
11
1010
10040
100040
1000040
10000040
100000040
1000000040
10000000040
100000000040
1000000000040

Power of 10Mod 61
11
1010
10039
100024
1000057
10000021
100000027
1000000026
10000000016
100000000038
1000000000014

Power of 10Mod 62
11
1010
10038
10008
1000018
10000056
10000002
1000000020
10000000014
100000000016
1000000000036

Power of 10Mod 63
11
1010
10037
100055
1000046
10000019
10000001
1000000010
10000000037
100000000055
1000000000046

Power of 10Mod 64
11
1010
10036
100040
1000016
10000032
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 65
11
1010
10035
100025
1000055
10000030
100000040
1000000010
10000000035
100000000025
1000000000055

Power of 10Mod 66
11
1010
10034
100010
1000034
10000010
100000034
1000000010
10000000034
100000000010
1000000000034

Power of 10Mod 67
11
1010
10033
100062
1000017
10000036
100000025
1000000049
10000000021
10000000009
1000000000023

Power of 10Mod 68
11
1010
10032
100048
100004
10000040
100000060
1000000056
10000000016
100000000024
1000000000036

Power of 10Mod 69
11
1010
10031
100034
1000064
10000019
100000052
1000000037
10000000025
100000000043
1000000000016

Power of 10Mod 70
11
1010
10030
100020
1000060
10000040
100000050
1000000010
10000000030
100000000020
1000000000060

Power of 10Mod 71
11
1010
10029
10006
1000060
10000032
100000036
100000005
10000000050
10000000003
1000000000030

Power of 10Mod 72
11
1010
10028
100064
1000064
10000064
100000064
1000000064
10000000064
100000000064
1000000000064

Power of 10Mod 73
11
1010
10027
100051
1000072
10000063
100000046
1000000022
1000000001
100000000010
1000000000027

Power of 10Mod 74
11
1010
10026
100038
1000010
10000026
100000038
1000000010
10000000026
100000000038
1000000000010

Power of 10Mod 75
11
1010
10025
100025
1000025
10000025
100000025
1000000025
10000000025
100000000025
1000000000025

Power of 10Mod 76
11
1010
10024
100012
1000044
10000060
100000068
1000000072
10000000036
100000000056
1000000000028

Power of 10Mod 77
11
1010
10023
100076
1000067
10000054
10000001
1000000010
10000000023
100000000076
1000000000067

Power of 10Mod 78
11
1010
10022
100064
1000016
1000004
100000040
1000000010
10000000022
100000000064
1000000000016

Power of 10Mod 79
11
1010
10021
100052
1000046
10000065
100000018
1000000022
10000000062
100000000067
1000000000038

Power of 10Mod 80
11
1010
10020
100040
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000

Power of 10Mod 81
11
1010
10019
100028
1000037
10000046
100000055
1000000064
10000000073
10000000001
1000000000010

Power of 10Mod 82
11
1010
10018
100016
1000078
10000042
100000010
1000000018
10000000016
100000000078
1000000000042

Power of 10Mod 83
11
1010
10017
10004
1000040
10000068
100000016
1000000077
10000000023
100000000064
1000000000059

Power of 10Mod 84
11
1010
10016
100076
100004
10000040
100000064
1000000052
10000000016
100000000076
100000000004

Power of 10Mod 85
11
1010
10015
100065
1000055
10000040
100000060
100000005
10000000050
100000000075
1000000000070

Power of 10Mod 86
11
1010
10014
100054
1000024
10000068
100000078
100000006
10000000060
100000000084
1000000000066

Power of 10Mod 87
11
1010
10013
100043
1000082
10000037
100000022
1000000046
10000000025
100000000076
1000000000064

Power of 10Mod 88
11
1010
10012
100032
1000056
10000032
100000056
1000000032
10000000056
100000000032
1000000000056

Power of 10Mod 89
11
1010
10011
100021
1000032
10000053
100000085
1000000049
10000000045
10000000005
1000000000050

Power of 10Mod 90
11
1010
10010
100010
1000010
10000010
100000010
1000000010
10000000010
100000000010
1000000000010

Power of 10Mod 91
11
1010
1009
100090
1000081
10000082
10000001
1000000010
1000000009
100000000090
1000000000081

Power of 10Mod 92
11
1010
1008
100080
1000064
10000088
100000052
1000000060
10000000048
100000000020
1000000000016

Power of 10Mod 93
11
1010
1007
100070
1000049
10000025
100000064
1000000082
10000000076
100000000016
1000000000067

Power of 10Mod 94
11
1010
1006
100060
1000036
10000078
100000028
1000000092
10000000074
100000000082
1000000000068

Power of 10Mod 95
11
1010
1005
100050
1000025
10000060
100000030
1000000015
10000000055
100000000075
1000000000085

Power of 10Mod 96
11
1010
1004
100040
1000016
10000064
100000064
1000000064
10000000064
100000000064
1000000000064

Power of 10Mod 97
11
1010
1003
100030
100009
10000090
100000027
1000000076
10000000081
100000000034
1000000000049

Power of 10Mod 98
11
1010
1002
100020
100004
10000040
10000008
1000000080
10000000016
100000000062
1000000000032

Power of 10Mod 99
11
1010
1001
100010
100001
10000010
10000001
1000000010
1000000001
100000000010
100000000001



Ken Ward's Mathematics Pages


Faster Arithmetic - by Ken Ward

Ken's book is packed with examples and explanations that enable you to discover more than 150 techniques to speed up your arithmetic and increase your understanding of numbers. Paperback and Kindle:
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Faster Arithmetic for Adults