Find the prime factorization of each number ()

891
23
504
230

Step-by-step explanation:

23 is a prime number. That fact informs the factorization of 23 and 230.

The sums of digits of the other two numbers are multiples of 9, so each is divisible by 9 = 3^2. Dividing 9 from each number puts the result in the range where your familiarity with multiplication tables comes into play.

  891 = 9 · 99 = 9 · 9 · 11 = 3^4 · 11

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  504 = 9 · 56 = 9 · 8 · 7 = 2^3 · 3^2 · 7

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  230 = 10 · 23 = 2 · 5 · 23

Comment on divisibility rules

Perhaps the easiest divisibility rule to remember is that a number is divisible by 9 if the sum of its digits is divisible by 9. That is also true for 3: if the sum of digits is divisible by 3, the number is divisible by 3. Another divisibility rule fall out from these: if an even number is divisible by 3, it is also divisible by 6. Of course any number ending in 0 or 5 is divisible by 5, and any number ending in 0 is divisible by 10.

Since 2, 3, and 5 are the first three primes, these rules can go a ways toward prime factorization if any of these primes are factors. That is, it can be helpful to remember these divisibility rules.

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

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step-by-step explanation:

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