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Fascinating Number Properties

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Subject: GCSE Maths
Last updated: 22/09/2010
Tags: gcse maths, inspirational figures
GCSE Maths

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Fascinating Number Properties

Mathematicians and non-mathematicians have been fascinated for centuries by the most remarkable and bizarre properties and patterns of numbers.

A few of these are presented here to get you started on a stimulating adventure in the world of mathematics.

 

Number 6

6 x 7 = 42

66 x 67 = 4422

666 x 667 = 444222

6666 x 6667 = 44442222

66666 x 66667 = 4444422222

666666 x 666667 = 444444222222

6666666 x 6666667 = 44444442222222

66666666 x 66666667 = 4444444422222222

666666666 x 666666667 = 444444444222222222

 

Number 7

1 x 7 + 3 = 10

14 x 7 + 2 = 100

142 x 7 + 6 = 1000

1428 x 7 + 4 = 10000

14285 x 7 + 5 = 100000

142857 x 7 + 1 = 1000000

1428571 x 7 + 3 = 10000000

14285714 x 7 + 2 = 100000000

1428571428 x 7 + 4 = 10000000000

 

Number 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

 

Without 8

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

 

Number 9

9 x 9 = 81

99 x 99 = 9801

999 x 999 = 998001

9999 x 9999 = 99980001

99999 x 99999 = 9999800001

999999 x 999999 = 999998000001

9999999 x 9999999 = 99999980000001

99999999 x 99999999 = 9999999800000001

999999999 x 999999999 = 999999998000000001

 

 Squared numbers

12 = 1

22 = 1+3

32 = 1+3+5

42 = 1+3+5+7

52 = 1+3+5+7+9

62 = 1+3+5+7+9+11

72 = 1+3+5+7+9+11+13

82 = 1+3+5+7+9+11+13+15

92 = 1+3+5+7+9+11+13+15+17

 

Cubed numbers

13 = 1

23 = 3+5

33 = 7+9+11

43 = 13+15+17+19

53 = 21+23+25+27+29

63 = 31+33+35+37+39+41

73 = 43+45+47+49+51+53+55

83 = 57+59+61+63+65+67+69+71

93 = 73+75+77+79+81+83+85+87+89

 




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