What are the factor pairs for 1 2 3 4 6 7 12 14 21 28 42 49 84 98 147 196 and 294?

Answer 1

There is no number with the given list as its only proper factors.

As 2 and 5 are both proper factors of the number, 10 must also be a proper factor of the number, but you have not listed it.

Dropping the proper factor 5 and adding the proper factor 21 allows the number to be 2 x 294 = 588.

All factors of a number have a pair which when multiplied together give the number.

The first proper factor of all numbers is 1 and would pair with the number itself. The second proper factor pairs with the last proper factor, the third with the second to last and so on. If this leaves one factor unpaired, the number is a perfect square of this factor.

For your list (corrected):

The number = 1 x number

= 2 x 294

= 3 x 196

= 4 x 147

= 6 x 98

= 7 x 84

= 12 x 49

= 14 x 42

= 21 x 28

For your list, the lowest number which has all those factors is 2940 which also has the extra proper factors: 10, 15, 20, 21, 30, 35, 60, 70, 105, 140, 210, 245, 420, 490, 588, 735, 980 & 1470

Another answer:

There's a problem here. There are two definitions of proper factors. One leaves out the number itself, and the other leaves out one and the number itself. Since you've included one, we'll go with the first definition. Since the last number has been removed, that would mean that the number you're looking for would be the product of the second number (2) and the second to last number (294) or the third number (3) and the third to last number (196) and so on. Both of these are 588. But the list you've notated is not the proper factors of 588. Take out the 5 and add a 21 and you will have listed the proper factors of 588.

Answer 2

1: 1

2: 1, 2

3: 1, 3

4: 1, 2, 4

6: 1, 2, 3, 6

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 8, 12, 24

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

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

Answer 3

(588,1)(294,2)(196,3)(147,4)(98,6)(84,7)(49,12)(42,14)(28,21)