How to express 648 as product of powers of their prime factors

Question

i need a step by step calculation about my question

Answer 1

Hi Mohammad!

 

All the answers so far have to do with figuring out factors for the specific number in this problem - 648, but one detail is being left out.

 

Suppose that the number in the problem is not 648 but a larger number,  is not even, not divisibile by 3, 5, 7,...   If you try all of these, then you could try 11 then 13.  But how high do you need to go before you decide that the number is prime and can't be divided by anything?  

 

Here's the deal.  If you take the number 648,  √648 = 25.456 .    The rule is - you don't need to try to divide 648 by a factor greater than 25.   That is, if it's not divisible by a number less than or equal to 25, then it's a prime number and can't be divided.

 

Why is this true?  Let's suppose that 648 was divisible by a number greater than 25, then if you divide it by that number the result would have to be less than 25; that's because multiplying any two numbers greater than 25 gets you a number greater than 648!  So if there is a factor greater than 25 then there is a factor less than 25 also.

 

 

 

 

Answer 2

2 | 648

2 | 324

2 | 162

3 | 81

3 | 27

3 | 9

3 | 3

     1

 

So 648 = 2^3 * 3^4

Answer 3

Factor the number to its prime constituents.

 

• Begin by reducing even numbers (divide by 2)
• Continue by recognizing other factors that have multiples

 

648=(2)(2)(2)(81)    (just keep dividing by 2 until you can no longer do it

648=(2)(2)(2)(9)(9)  (9 is still not prime)

648=(2)(2)(2)(3)(3)(3)(3)   <---- We're DONE!!  Now place in exponential form (powers of primes)

 

648=2³3⁴

 

Answer 4

648 is divisible by 2, 3, 4, 6, and 8 to name a few factors.

648=8*81

648=2*2*2*9*9

648=2*2*2*3*3*3*3

648=2^3*3^4