Question

Find the prime factorization of each number (please)89123504230

Answer 1

Answer:

• 891 = 3^4 · 11
• 23 = 23
• 504 = 2^3 · 3^2 · 7
• 230 = 2 · 5 · 23

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

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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.