Ordering a sequence of numbers given under the form $2^p 3^q 5^r$

Question

If $w = 2^{230} × 3^{234} × 5^{236}$, $x = 2^{232} × 3^{233} × 5^{235}$,$y = 2^{230} × 3^{233} × 5^{235}$ and $z = 2^{231} × 3^{234} × 5^{235}$ then the order from smallest to largest is:

At first, I thought that the one of the largest exponent on the bigger number would be greater, however that turned out to be incorrect. may you please give me an accurate way to do this question

Answer 1

Hint:

Take $2^{230}\times3^{233}\times5^{235}$ common from $w,x,y,z$, and then compare.

Answer 2

Assuming $a = 2^{230} \times 3^{233} \times 5^{235}$

Then: $w = a \cdot 3 \cdot 5$, $x = a \cdot 2 \cdot 2$, $y = a$ and $z = a \cdot 2 \cdot 3$

Therefore: $y < x < z < w$.