Page 12 - NUMINO Challenge_C1
P. 12
Basic Concepts The Secret of 142857
We can find a number of interesting patterns when we multiply or add using
the six numbers: 142857.
142857 7 999999 142 857 999 14 28 57 99
Example Here are the results of multiplying 142857 by a number from 1 to
6. Find the pattern and fill in the blank.
142857 1 142857
142857 2 285714
142857 3 428571
142857 4
142857 5 714285
142857 6 857142
Class Notes
The products of 142857 and the numbers 1, 2, and 3 are shown below.
1 1 1
74 74 74
52 52 52
8 8 8
142857 1 14285 7 142857 2 28571 4 142857 3 42857 1
Numbers 1, 4, , , , and appear in (clockwise, counterclockwise) order.
Since the number in the ones place of 142857 4 is , the product is .
9Number and Operations
We can find a number of interesting patterns when we multiply or add using
the six numbers: 142857.
142857 7 999999 142 857 999 14 28 57 99
Example Here are the results of multiplying 142857 by a number from 1 to
6. Find the pattern and fill in the blank.
142857 1 142857
142857 2 285714
142857 3 428571
142857 4
142857 5 714285
142857 6 857142
Class Notes
The products of 142857 and the numbers 1, 2, and 3 are shown below.
1 1 1
74 74 74
52 52 52
8 8 8
142857 1 14285 7 142857 2 28571 4 142857 3 42857 1
Numbers 1, 4, , , , and appear in (clockwise, counterclockwise) order.
Since the number in the ones place of 142857 4 is , the product is .
9Number and Operations
