What are all the factors of 72?

Answer 1

The factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

I find factors in pairs, It will look like more work than it is, because I will explain how I am doing these steps. I do most of the work without writing it down. I'll put the explanation in black in [brackets] and the answer in #color(blue)"blue"#.
I'll proceed by starting with #1# on the left and checking each number in order until either I get to a number already on the right or I get to a number greater than the square root of 72.
#color(blue)(1 xx 72)#

[I divide 72 by 2 because I can see it is divisible by 2; this gives me the next pair.]

#color(blue)(2 xx 36)#
[Now we check 3 and we get the next pair.] [I use a little trick for this. I know that 36 is divisible by 3 and #36 = 3xx12#. This tells me that #72 = 2xx3xx12#, so I know that #72 = 3xx2xx12 = 3xx24#]
#color(blue)(3 xx 24)#
[Now we need to check 4. Up above, we got #72 = 2xx36# since #36 = 2xx18#, we see that #72 = 2xx2xx18 = 4xx18#]
#color(blue)(4 xx 18)#

[The number five is the next to be checked, but 72 is not divisible by five. I usually write a number before I check, so I cross out the ones that don't apply.]

#color(blue)cancel(5)#
{Move on to 6. Looking above I want to 'build' a 6 by multiplying a number on the left times a factor of the number to its right. I see two ways to do that: #2xx36 = 2xx3xx12 = 6xx12# and #3xx24 = 3xx2xx12=6xx12#. (Or maybe you just know that #6xx12=72#.)]
#color(blue)(6 xx 12)#

[72 cannot be divided by 7]

#color(blue)cancel(7)#
{#4xx18 = 4xx2xx9=8xx9#]
#color(blue)(8 xx 9)#

[Is that clear? Any factor of 72 greater than 9 must be multiplied by something less than 8 to get 72. But we've checked all the numbers up to and including 8. So we're finished.] [And that's all. 9 and the factors that are greater than 9 are already written on the right in the list of pairs above.]

[If we were doing this for #39# we would get #1xx39# and #3xx13#, then we cross off every number until we notice that #7xx7 = 49#. If 39 had a factor greater than 7 it would have to be multiplied by something less that 7 (otherwise we get 49 or more). So we would be finished.]
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Answer 2

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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