What three numbers multiply to get 126?

What three numbers multiply to get 126? In other words, you want to know all the combinations of 3 numbers that can be multiplied to get 126. You want to know what all the question marks in the equation below can be in order for the equation to be true:

? × ? × ? = 126

First, note that all numbers must be 126 or less, which means that there are 126 × 126 × 126 possible solutions. Thus, to get the answer to "What three numbers multiply to get 126?" we looked at 2,000,376 different combinations to see which ones equal 126.

When we looked at all those combinations, we found 54 different combinations of 3 numbers that equal 126 when multiplied together. Here are all 3 number combinations that you can multiply to get 126:

126 × 1 × 1 = 126
63 × 2 × 1 = 126
63 × 1 × 2 = 126
42 × 3 × 1 = 126
42 × 1 × 3 = 126
21 × 6 × 1 = 126
21 × 3 × 2 = 126
21 × 2 × 3 = 126
21 × 1 × 6 = 126
18 × 7 × 1 = 126
18 × 1 × 7 = 126
14 × 9 × 1 = 126
14 × 3 × 3 = 126
14 × 1 × 9 = 126
9 × 14 × 1 = 126
9 × 7 × 2 = 126
9 × 2 × 7 = 126
9 × 1 × 14 = 126
7 × 18 × 1 = 126
7 × 9 × 2 = 126
7 × 6 × 3 = 126
7 × 3 × 6 = 126
7 × 2 × 9 = 126
7 × 1 × 18 = 126
6 × 21 × 1 = 126
6 × 7 × 3 = 126
6 × 3 × 7 = 126
6 × 1 × 21 = 126
3 × 42 × 1 = 126
3 × 21 × 2 = 126
3 × 14 × 3 = 126
3 × 7 × 6 = 126
3 × 6 × 7 = 126
3 × 3 × 14 = 126
3 × 2 × 21 = 126
3 × 1 × 42 = 126
2 × 63 × 1 = 126
2 × 21 × 3 = 126
2 × 9 × 7 = 126
2 × 7 × 9 = 126
2 × 3 × 21 = 126
2 × 1 × 63 = 126
1 × 126 × 1 = 126
1 × 63 × 2 = 126
1 × 42 × 3 = 126
1 × 21 × 6 = 126
1 × 18 × 7 = 126
1 × 14 × 9 = 126
1 × 9 × 14 = 126
1 × 7 × 18 = 126
1 × 6 × 21 = 126
1 × 3 × 42 = 126
1 × 2 × 63 = 126
1 × 1 × 126 = 126

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What three numbers multiply to get 127?
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