Followup: Multiplicity?

Question

Hello, I'm a CIS major taking Discrete Structures and Im having problems figuring this problem out..

Are the following correct?

The multiplicty of 2 in 258 is 3?
The multiplicity of 3 in 168 is 1?
The multiplicty of 3 in 5040 is 2?
The multiplicty of 5 in 5120 is 1?
The multiplicty of 6 in 168 is 1?**

**im not sure of this one

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Number 1 was supposed to be:
The multiplicty of 2 in 168 is 3?
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Answer 1

Hello there. If "multiplicity" means the recuring factors then they are all correct except the first, which has only one 2.

258 = 2 x 3 x 43
168 = 2 x 2 x 2 x 3 x 7 = 6 x 3 x 7 = 2 x 2 x 6 x 7
5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5
5120 = 2 x 2 x 5 x 31

an easy way to factor is to start with the lowest prime number (2) and start dividing. Work your way up until you run out of prime numbers that will divide into it. In the case where you're looking for a composite number (the 6 in 168) just see how many times you can make that number from your primes, as I've shown in the second one above.

Good luck!

Answer 2

These are all correct except the first one.
The multiplicity of 2 in 258 is 1, not 3.
The highest power of 2 dividing 258 is 1.
The last one is right, because the multiplicity of 3
in 168 is 1.

Answer 3

I am not familiar with this use of "multiplicity" but I guess it means the number of times the digit occurs as a factor.If that is correct the multiplicity of 2 in 258 is 1. The others are correct.

Answer 4

First one: not correct
Second one: correct
Third one: correct
Fourth one: correct
Fifth one: correct

To check if the multiplicity of n in p is k, see if p is divisible by n^k. You'll see that this is not the case with the first one.