## factor

#### 1

$E$ is similar to $F$ but scaled by a factor 1/3.

Thus $E$ is similar to $F$ with a scale factor 1/3.

The only additional feature is the appearance of a factor of 2.

Thus we need only alter our constants by a factor of 2 to deal with this case.

This accounts for the factor 1/2 in (4).

#### 2

The map $f$ factors through the space $X$.

We can factor $g$ into a product of irreducible elements.

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