mathematics

Ken Ward's Mathematics Pages

Number Theory

See Divisibility for an explanation

Power of 10	Mod 2
1	1
10	0
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 3
1	1
10	1
100	1
1000	1
10000	1
100000	1
1000000	1
10000000	1
100000000	1
1000000000	1
10000000000	1

Power of 10	Mod 4
1	1
10	2
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 5
1	1
10	0
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 6
1	1
10	4
100	4
1000	4
10000	4
100000	4
1000000	4
10000000	4
100000000	4
1000000000	4
10000000000	4

Power of 10	Mod 7
1	1
10	3
100	2
1000	6
10000	4
100000	5
1000000	1
10000000	3
100000000	2
1000000000	6
10000000000	4

Power of 10	Mod 8
1	1
10	2
100	4
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 9
1	1
10	1
100	1
1000	1
10000	1
100000	1
1000000	1
10000000	1
100000000	1
1000000000	1
10000000000	1

Power of 10	Mod 10
1	1
10	0
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 11
1	1
10	10
100	1
1000	10
10000	1
100000	10
1000000	1
10000000	10
100000000	1
1000000000	10
10000000000	1

Power of 10	Mod 12
1	1
10	10
100	4
1000	4
10000	4
100000	4
1000000	4
10000000	4
100000000	4
1000000000	4
10000000000	4

Power of 10	Mod 13
1	1
10	10
100	9
1000	12
10000	3
100000	4
1000000	1
10000000	10
100000000	9
1000000000	12
10000000000	3

Power of 10	Mod 14
1	1
10	10
100	2
1000	6
10000	4
100000	12
1000000	8
10000000	10
100000000	2
1000000000	6
10000000000	4

Power of 10	Mod 15
1	1
10	10
100	10
1000	10
10000	10
100000	10
1000000	10
10000000	10
100000000	10
1000000000	10
10000000000	10

Power of 10	Mod 16
1	1
10	10
100	4
1000	8
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 17
1	1
10	10
100	15
1000	14
10000	4
100000	6
1000000	9
10000000	5
100000000	16
1000000000	7
10000000000	2

Power of 10	Mod 18
1	1
10	10
100	10
1000	10
10000	10
100000	10
1000000	10
10000000	10
100000000	10
1000000000	10
10000000000	10

Power of 10	Mod 19
1	1
10	10
100	5
1000	12
10000	6
100000	3
1000000	11
10000000	15
100000000	17
1000000000	18
10000000000	9

Power of 10	Mod 20
1	1
10	10
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 21
1	1
10	10
100	16
1000	13
10000	4
100000	19
1000000	1
10000000	10
100000000	16
1000000000	13
10000000000	4

Power of 10	Mod 22
1	1
10	10
100	12
1000	10
10000	12
100000	10
1000000	12
10000000	10
100000000	12
1000000000	10
10000000000	12

Power of 10	Mod 23
1	1
10	10
100	8
1000	11
10000	18
100000	19
1000000	6
10000000	14
100000000	2
1000000000	20
10000000000	16

Power of 10	Mod 24
1	1
10	10
100	4
1000	16
10000	16
100000	16
1000000	16
10000000	16
100000000	16
1000000000	16
10000000000	16

Power of 10	Mod 25
1	1
10	10
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 26
1	1
10	10
100	22
1000	12
10000	16
100000	4
1000000	14
10000000	10
100000000	22
1000000000	12
10000000000	16

Power of 10	Mod 27
1	1
10	10
100	19
1000	1
10000	10
100000	19
1000000	1
10000000	10
100000000	19
1000000000	1
10000000000	10

Power of 10	Mod 28
1	1
10	10
100	16
1000	20
10000	4
100000	12
1000000	8
10000000	24
100000000	16
1000000000	20
10000000000	4

Power of 10	Mod 29
1	1
10	10
100	13
1000	14
10000	24
100000	8
1000000	22
10000000	17
100000000	25
1000000000	18
10000000000	6

Power of 10	Mod 30
1	1
10	10
100	10
1000	10
10000	10
100000	10
1000000	10
10000000	10
100000000	10
1000000000	10
10000000000	10

Power of 10	Mod 31
1	1
10	10
100	7
1000	8
10000	18
100000	25
1000000	2
10000000	20
100000000	14
1000000000	16
10000000000	5

Power of 10	Mod 32
1	1
10	10
100	4
1000	8
10000	16
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 33
1	1
10	10
100	1
1000	10
10000	1
100000	10
1000000	1
10000000	10
100000000	1
1000000000	10
10000000000	1

Power of 10	Mod 34
1	1
10	10
100	32
1000	14
10000	4
100000	6
1000000	26
10000000	22
100000000	16
1000000000	24
10000000000	2

Power of 10	Mod 35
1	1
10	10
100	30
1000	20
10000	25
100000	5
1000000	15
10000000	10
100000000	30
1000000000	20
10000000000	25

Power of 10	Mod 36
1	1
10	10
100	28
1000	28
10000	28
100000	28
1000000	28
10000000	28
100000000	28
1000000000	28
10000000000	28

Power of 10	Mod 37
1	1
10	10
100	26
1000	1
10000	10
100000	26
1000000	1
10000000	10
100000000	26
1000000000	1
10000000000	10

Power of 10	Mod 38
1	1
10	10
100	24
1000	12
10000	6
100000	22
1000000	30
10000000	34
100000000	36
1000000000	18
10000000000	28

Power of 10	Mod 39
1	1
10	10
100	22
1000	25
10000	16
100000	4
1000000	1
10000000	10
100000000	22
1000000000	25
10000000000	16

Power of 10	Mod 40
1	1
10	10
100	20
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 41
1	1
10	10
100	18
1000	16
10000	37
100000	1
1000000	10
10000000	18
100000000	16
1000000000	37
10000000000	1

Power of 10	Mod 42
1	1
10	10
100	16
1000	34
10000	4
100000	40
1000000	22
10000000	10
100000000	16
1000000000	34
10000000000	4

Power of 10	Mod 43
1	1
10	10
100	14
1000	11
10000	24
100000	25
1000000	35
10000000	6
100000000	17
1000000000	41
10000000000	23

Power of 10	Mod 44
1	1
10	10
100	12
1000	32
10000	12
100000	32
1000000	12
10000000	32
100000000	12
1000000000	32
10000000000	12

Power of 10	Mod 45
1	1
10	10
100	10
1000	10
10000	10
100000	10
1000000	10
10000000	10
100000000	10
1000000000	10
10000000000	10

Power of 10	Mod 46
1	1
10	10
100	8
1000	34
10000	18
100000	42
1000000	6
10000000	14
100000000	2
1000000000	20
10000000000	16

Power of 10	Mod 47
1	1
10	10
100	6
1000	13
10000	36
100000	31
1000000	28
10000000	45
100000000	27
1000000000	35
10000000000	21

Power of 10	Mod 48
1	1
10	10
100	4
1000	40
10000	16
100000	16
1000000	16
10000000	16
100000000	16
1000000000	16
10000000000	16

Power of 10	Mod 49
1	1
10	10
100	2
1000	20
10000	4
100000	40
1000000	8
10000000	31
100000000	16
1000000000	13
10000000000	32

Power of 10	Mod 50
1	1
10	10
100	0
1000	0
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 51
1	1
10	10
100	49
1000	31
10000	4
100000	40
1000000	43
10000000	22
100000000	16
1000000000	7
10000000000	19

Power of 10	Mod 52
1	1
10	10
100	48
1000	12
10000	16
100000	4
1000000	40
10000000	36
100000000	48
1000000000	12
10000000000	16

Power of 10	Mod 53
1	1
10	10
100	47
1000	46
10000	36
100000	42
1000000	49
10000000	13
100000000	24
1000000000	28
10000000000	15

Power of 10	Mod 54
1	1
10	10
100	46
1000	28
10000	10
100000	46
1000000	28
10000000	10
100000000	46
1000000000	28
10000000000	10

Power of 10	Mod 55
1	1
10	10
100	45
1000	10
10000	45
100000	10
1000000	45
10000000	10
100000000	45
1000000000	10
10000000000	45

Power of 10	Mod 56
1	1
10	10
100	44
1000	48
10000	32
100000	40
1000000	8
10000000	24
100000000	16
1000000000	48
10000000000	32

Power of 10	Mod 57
1	1
10	10
100	43
1000	31
10000	25
100000	22
1000000	49
10000000	34
100000000	55
1000000000	37
10000000000	28

Power of 10	Mod 58
1	1
10	10
100	42
1000	14
10000	24
100000	8
1000000	22
10000000	46
100000000	54
1000000000	18
10000000000	6

Power of 10	Mod 59
1	1
10	10
100	41
1000	56
10000	29
100000	54
1000000	9
10000000	31
100000000	15
1000000000	32
10000000000	25

Power of 10	Mod 60
1	1
10	10
100	40
1000	40
10000	40
100000	40
1000000	40
10000000	40
100000000	40
1000000000	40
10000000000	40

Power of 10	Mod 61
1	1
10	10
100	39
1000	24
10000	57
100000	21
1000000	27
10000000	26
100000000	16
1000000000	38
10000000000	14

Power of 10	Mod 62
1	1
10	10
100	38
1000	8
10000	18
100000	56
1000000	2
10000000	20
100000000	14
1000000000	16
10000000000	36

Power of 10	Mod 63
1	1
10	10
100	37
1000	55
10000	46
100000	19
1000000	1
10000000	10
100000000	37
1000000000	55
10000000000	46

Power of 10	Mod 64
1	1
10	10
100	36
1000	40
10000	16
100000	32
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 65
1	1
10	10
100	35
1000	25
10000	55
100000	30
1000000	40
10000000	10
100000000	35
1000000000	25
10000000000	55

Power of 10	Mod 66
1	1
10	10
100	34
1000	10
10000	34
100000	10
1000000	34
10000000	10
100000000	34
1000000000	10
10000000000	34

Power of 10	Mod 67
1	1
10	10
100	33
1000	62
10000	17
100000	36
1000000	25
10000000	49
100000000	21
1000000000	9
10000000000	23

Power of 10	Mod 68
1	1
10	10
100	32
1000	48
10000	4
100000	40
1000000	60
10000000	56
100000000	16
1000000000	24
10000000000	36

Power of 10	Mod 69
1	1
10	10
100	31
1000	34
10000	64
100000	19
1000000	52
10000000	37
100000000	25
1000000000	43
10000000000	16

Power of 10	Mod 70
1	1
10	10
100	30
1000	20
10000	60
100000	40
1000000	50
10000000	10
100000000	30
1000000000	20
10000000000	60

Power of 10	Mod 71
1	1
10	10
100	29
1000	6
10000	60
100000	32
1000000	36
10000000	5
100000000	50
1000000000	3
10000000000	30

Power of 10	Mod 72
1	1
10	10
100	28
1000	64
10000	64
100000	64
1000000	64
10000000	64
100000000	64
1000000000	64
10000000000	64

Power of 10	Mod 73
1	1
10	10
100	27
1000	51
10000	72
100000	63
1000000	46
10000000	22
100000000	1
1000000000	10
10000000000	27

Power of 10	Mod 74
1	1
10	10
100	26
1000	38
10000	10
100000	26
1000000	38
10000000	10
100000000	26
1000000000	38
10000000000	10

Power of 10	Mod 75
1	1
10	10
100	25
1000	25
10000	25
100000	25
1000000	25
10000000	25
100000000	25
1000000000	25
10000000000	25

Power of 10	Mod 76
1	1
10	10
100	24
1000	12
10000	44
100000	60
1000000	68
10000000	72
100000000	36
1000000000	56
10000000000	28

Power of 10	Mod 77
1	1
10	10
100	23
1000	76
10000	67
100000	54
1000000	1
10000000	10
100000000	23
1000000000	76
10000000000	67

Power of 10	Mod 78
1	1
10	10
100	22
1000	64
10000	16
100000	4
1000000	40
10000000	10
100000000	22
1000000000	64
10000000000	16

Power of 10	Mod 79
1	1
10	10
100	21
1000	52
10000	46
100000	65
1000000	18
10000000	22
100000000	62
1000000000	67
10000000000	38

Power of 10	Mod 80
1	1
10	10
100	20
1000	40
10000	0
100000	0
1000000	0
10000000	0
100000000	0
1000000000	0
10000000000	0

Power of 10	Mod 81
1	1
10	10
100	19
1000	28
10000	37
100000	46
1000000	55
10000000	64
100000000	73
1000000000	1
10000000000	10

Power of 10	Mod 82
1	1
10	10
100	18
1000	16
10000	78
100000	42
1000000	10
10000000	18
100000000	16
1000000000	78
10000000000	42

Power of 10	Mod 83
1	1
10	10
100	17
1000	4
10000	40
100000	68
1000000	16
10000000	77
100000000	23
1000000000	64
10000000000	59

Power of 10	Mod 84
1	1
10	10
100	16
1000	76
10000	4
100000	40
1000000	64
10000000	52
100000000	16
1000000000	76
10000000000	4

Power of 10	Mod 85
1	1
10	10
100	15
1000	65
10000	55
100000	40
1000000	60
10000000	5
100000000	50
1000000000	75
10000000000	70

Power of 10	Mod 86
1	1
10	10
100	14
1000	54
10000	24
100000	68
1000000	78
10000000	6
100000000	60
1000000000	84
10000000000	66

Power of 10	Mod 87
1	1
10	10
100	13
1000	43
10000	82
100000	37
1000000	22
10000000	46
100000000	25
1000000000	76
10000000000	64

Power of 10	Mod 88
1	1
10	10
100	12
1000	32
10000	56
100000	32
1000000	56
10000000	32
100000000	56
1000000000	32
10000000000	56

Power of 10	Mod 89
1	1
10	10
100	11
1000	21
10000	32
100000	53
1000000	85
10000000	49
100000000	45
1000000000	5
10000000000	50

Power of 10	Mod 90
1	1
10	10
100	10
1000	10
10000	10
100000	10
1000000	10
10000000	10
100000000	10
1000000000	10
10000000000	10

Power of 10	Mod 91
1	1
10	10
100	9
1000	90
10000	81
100000	82
1000000	1
10000000	10
100000000	9
1000000000	90
10000000000	81

Power of 10	Mod 92
1	1
10	10
100	8
1000	80
10000	64
100000	88
1000000	52
10000000	60
100000000	48
1000000000	20
10000000000	16

Power of 10	Mod 93
1	1
10	10
100	7
1000	70
10000	49
100000	25
1000000	64
10000000	82
100000000	76
1000000000	16
10000000000	67

Power of 10	Mod 94
1	1
10	10
100	6
1000	60
10000	36
100000	78
1000000	28
10000000	92
100000000	74
1000000000	82
10000000000	68

Power of 10	Mod 95
1	1
10	10
100	5
1000	50
10000	25
100000	60
1000000	30
10000000	15
100000000	55
1000000000	75
10000000000	85

Power of 10	Mod 96
1	1
10	10
100	4
1000	40
10000	16
100000	64
1000000	64
10000000	64
100000000	64
1000000000	64
10000000000	64

Power of 10	Mod 97
1	1
10	10
100	3
1000	30
10000	9
100000	90
1000000	27
10000000	76
100000000	81
1000000000	34
10000000000	49

Power of 10	Mod 98
1	1
10	10
100	2
1000	20
10000	4
100000	40
1000000	8
10000000	80
100000000	16
1000000000	62
10000000000	32

Power of 10	Mod 99
1	1
10	10
100	1
1000	10
10000	1
100000	10
1000000	1
10000000	10
100000000	1
1000000000	10
10000000000	1

Ken Ward's Mathematics Pages

Faster Arithmetic - by Ken Ward

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