Answer:
8z+15
Step-by-step explanation:
A factor pair is two numbers that can be multiplied to get a number.
With any number, we know that 1*itself is a factor pair. So
1*64
The number in the ones place, 4, is even, so we know that 64 is a multiple of 2. Half of 64 is 32, so
2*32
To find out if 3 is a factor of 64, we can add 6+4. If the answer is a multiple of 3, then we know that the number itself is a multiple of 3. Because 6+4=10, and 10 is not a multiple of 3, we know that 64 is not a multiple of 3.
If 2 is not a factor of a number, then we know that 4 (2*2) cannot be a factor. Because 2 is a factor of 64, then 4 might be as well. To discover whether or not 4 is a factor of 64, we can look at the number above multiplied by 2 to equal 64 (32) and see if it divides by 2 evenly, or we can half 64 and then half it again. If either answer is a whole number, then we know that the answer*4 equals 64, and that 64 is a multiple of 4. Because half of 32 is 16, a whole number, we know that
4*16=64
Because 64 does not have a 0 or 5 in the one's place, we know that it cannot be a multiple of 5.
Because 64 is not a multiple of 3, we know it cannot be a multiple of 6, because 6 is 2*3.
I happen to be familiar with my times tables, so I can tell that the multiples of 7 are 63 and 70, but not 64.
I don't know if 64 is a multiple of 8 off the top of my head, but I can count by 8s and see if 64 comes up: 8, 16, 24, 32, 40, 48, 56, 64, 72 - I can go on, but we can already see that 64 is a multiple of 8, so 8 is a factor of 64. If we count the number of 8s I can see that there are 8 of them when we get to 64. In other words,
8*8=64
Because we have gotten to a factor pair that is the same 2 number multiplied by each other (the square root) we know that we have found all factor pairs of 64.
Any odd multiple of 3 would be the counterexample of the given conjecture.
That is 3(2n - 1), for any natural number n, will be divisible by 3 but not divisible by 6 as 2 is not a factor.
<u>Examples:</u>
3(3) = 9
3(5) = 15
3(7) = 21 are some examples.
