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Why aren't all odd numbers divisible by 3?
Because not all odd numbers are multiples of 3 - I have shown you below that this is the case and you can see some multiples of 3 are even and some are odd and you can also see that there are even and odd numbers BETWEEN the multiples of 3. 1 (odd) 2 (even) 1*3 =3 (odd) 4 (even) 5 (odd) 2*3 = 6 (even) 7 (odd) 8 (even) 3*3 = 9 (odd) 10 (even) 11 (odd) 4*3 = 12 (even)
What factors produce only odd multiples?
No number will produce only odd multiples, as any multiple of an even number will always be even. Proofs can be easily created of such a fact.
What are the five odd multiples of 3?
The are: 3 9 15 21 and 27
Why can't a number ending in 3 be a multiple of 4?
Even numbers are the multiples of 2 and are those numbers which end with one of {0, 2, 4, 6, 8}; odd numbers are those which are not multiples of two and are those numbers which end with {1, 3, 5, 7, 9}. When an even number is multiplied by an even or odd number the result is always an even number. 4 is an even number; thus all its multiples are even numbers. Any number that ends with a 3 is an odd number. There are no numbers which are both odd and even; therefore no multiple of 4 can end in a 3.
What do you notice about the multiples of 3?
When u continue to multiply by 3 u will see that all of the numbers will be EVEN or ODD.
