Patterns of Numbers Flashcards
Look for pattern
eg patterns in remainders
Powers of 0
0 (as base) to power of anything is 0
Powers of 1
1 (as base) to power of anything is 1
Powers of 2
2 (as base) to power of anything follows pattern (for units digit) of 2 - 4 - 6- 8
Powers of 3
3 (as base) to power of anything follows pattern (for units digit) of 3 - 9 - 7- 1
Powers of 4
4 (as base) to power of anything follows pattern (for units digit) of 4- 6. All odd is 4 and all even is 6
Powers of 5
5 (as base) to power of anything has units digit of 5
Powers of 6
6 (as base) to power of anything has units digit of 6
Powers of 7
7 (as base) to power of anything follows pattern (for units digit) of 7 - 9 - 3- 1
Powers of 8
8 (as base) to power of anything follows pattern (for units digit) of 8-4-2- 6.
Powers of 9
9 (as base) to power of anything follows pattern (for units digit) of 9- 1. All odd is 9 and all even is 1
For bases above 9, when working out value when raised to various powers…
…. just look at units digit
when a number is divided by 10,
the remainder is the units digit of the number
when a number is divided by 100
the remainder is the last two digit of the number
when integers with same units digit divided by 5…..
same remainder (is constant)
Evenly spaced set is
one in which numbers increase by same amount - so each two consecutive numbers, difference is the same
two consecutive integers
will never share same prime factors
so GCF of two consecutive integers
is never greater than 1
