All the integer factor pairs of 180

Question

I Want To Know 

Answer 1

1 is a factor of every number

every number is a factor of itself

 1 and 180 are factors

using rules for divisibility...

180 is even so 2 is a factor

180/2=90

2 and 90 are factors

1+8+0=9 and 9 is divisible by 3 so 3 is a factor

180/3=60

3 and 60 are factors

the number formed by the 2 right-most digits (80) is divisible by 4

180/4=45

4 and 45 are factors

180 hos a 0 in the ones place so 180 is divisible by 5

180/5=36

5 and 36 are factors

180 is divisible by both 2 and 3 so it is divisible by 2*3=6

180/6=30

6 and 30 are factors

divisibility by 7: subtract the ones digit, divide by 10, subtract 2 times the original ones digit-if you get a number divisible by 7 then the original number is divisible by 7

180-0=180, 180/10=18, 18-2*0=18 but 18 is not divisible by 7

to be divisible by 8 the number formed by the 3 right-most digits must be divisible by 8 but you have a 3-digit number and 180 is not divisible by 8

1+8+0=9 and 9 is divisible by 9 so 180 is divisible by 9

180/9=20

9 and 20 are factors

180 has a 0 in the ones place so 180 is divisible by 10

180/10=18

10 and 18 are factors

alternate the digits with - and + for divisibility by 11

1-8+0=-7 and -7 is not divisible by 11

180 is divisible by both 3 and 4 so it is divisible by 3*4=12

180/12=15

12 and 15 are factors

notice that the pairs keep getting closer and closer to each other

between 12 and 15 are 13 and 14

180 is not divisible by 13 and not divisible by 14 so you are done

you can google the rules for 13 and the rule for 14 is divisibility by both 2 and 7

 

Answer 2

The factors of 180 are:  1*2*2*3*3*5.

 

So, all the possible groupings of these numbers that create two-factor pairs:

1*180

2*90

3*60           (1*3) * (2*2*3*5)

4*45 

5*36

6*30

9*20

10*18

12*15

 

Since (-1)*(-1) =1, the factors may all be multiplied by (-1) also.

 

Answer 3

1,180

2,90

3,60

4,45

5,36

6,30

9,20

10,18

12,15

then we have the same list except each one is negative. 

Answer 4

To find all the integer factor pairs of 180, you first find all the positive factor pairs.  Start with 1, then move onto 2, and so on.  If it divides evenly, then the divisor and the quotient are a factor pair.  Keep going until you repeat a number already found, and you've got all pairs.  To find the rest, simple list the negative versions of each pair.  (i.e. since 1 and 180 are a pair, so it -1 and -180).  

 

There are going to be a lot of pairs, but you can do it.