What are the factors of 40?

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May 12, 2016

Answer:

The factors are #1#, #2#, #4#, #5#, #8#, #10#, #20#, #40#

Explanation:

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 40.

#color(blue)(1 xx 40)#

[I see that 40 is divisible by 2, and do the division to get the next pair]

#color(blue)(2 xx 20)#

[Now we check 3. But 40 is not divisible by 3. I usually write a number before I check, so if a number is not a factor, I cross it out.]]

#color(blue)cancel(3)#

[Now we need to check 4. Up above, we got #40 = 2xx20# since #20 = 2xx10#, we see that #40 = 2xx2xx10 = 4xx10#]

#color(blue)(4 xx 10)#

[The next number to check is 5. We can either divide #40 -: 5# to get #8# or split up the #10# in the last factor pair: #40 = 4xx10 = 4xx2xx5=8xx5#]

#color(blue)(5xx8)#

{Move on to 6. But 40 is not divisible by 6. -- 6 is not a factor of 40.

#color(blue)cancel(6)#

[40 is not divisible by 7.]

#color(blue)cancel(7)#

The next number, #8#, already appears on the list above (on the right).
For numbers greater than #8# to be factors of #40# they would have to be multiplied by something less than the #5# we use in #8xx5=40#. We've already checked the smaller numbers, so we're done.

The factors are #1#, #2#, #4#, #5#, #8#, #10#, #20#, #40#

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