In each of these questions, write the given number as a product of powers of primes in ascending order.
\n\nGive your answer in list form, where
\nthe 1st element represents the power of 2
\nthe 2nd element represents the power of 3
\nthe 3rd element represents the power of 5
\nthe 4th element represents the power of 7
\n\nFor example
\n$210=2\\times3\\times5\\times7$ we would give our answer as $[1,1,1,1]$
\n$63=3^2\\times7$ we would give our answer as $[0,2,0,1]$
\n$750=2\\times3\\times5^3$ we would give our answer as $[1,1,3,0]$
\n", "advice": "To find the prime factorisation of a number, keep breaking that number down into pairs of factors until all number written down are primes.
\ne.g. To find the prime factorisation of $2450$ we could note that
\n$2450 = 245 \\times 10$
\n$2450=245 \\times \\underline{5} \\times \\underline{2}$
\n$2450=\\underline{5} \\times 49 \\times \\underline{5}\\times \\underline{2}$
\n$2450=\\underline{5} \\times \\underline{7} \\times \\underline{7} \\times \\underline{5} \\times \\underline{2}$
\nwhere we have underlined the primes as we go along.
\nRewriting this in ascending order of primes, we obtain $2450 = 2 \\times 5 \\times 5 \\times 7 \\times 7$
\nwhich we can also write as $2450 = 2 \\times 5^2 \\times 7^2$
\n\n\n(a) Applying a similar method to the given questions, we can obtain:
\n\nWe can write the given numbers as products of prime factors as follows:
\n$\\var{x}=\\var{show_factors(x)}$
\n$\\var{y}=\\var{show_factors(y)}$
\n$\\var{z}=\\var{show_factors(z)}$
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