Math Help Question

[ststern45]

I purchased a software program and trying to figure out the calculations from a range of numbers.

The numbers are the following: 14 16 24 29 30
The answer is 9 according to the program calculation
The explanation is the following:
"The amount of multipliers which are equal to 2 in the range of cells"
In addition the help file: amount of factor 2 - The quantity of the factor = 2 of the numbers in the range

Example 2:
The numbers are the following: 4 5 9 20 28
The answer is 6 according to the program calculation

Example 3:
The numbers are the following: 8 16 18 19 22
The answer is 9 according the the program calculation

Example 4:
The numbers are the following: 8 12 16 17 26
The answer is 10 according the the program calculation

I'm trying figure out how the calculations correspond to the explanation from the help file and the given numbers.

Kudos to those who can figure this out.

Thanks in advance!!

Are the Factors of 2? = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

 

[Eric W]

Example 1:
14, 16, 24, 29, 30

=

7*2^1, 2^4, 3*2^3, 23*2^0, 15*2^1

add all the exponents of 2 =
1 + 4 + 3 + 0 + 1 = 9

 

[ststern45]

Thanks you Eric.
Very much appreciated!!

 

[johnnyL]

Are the Factors of 2? = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

The factors of 2 are 1,2
The factors of 3 are 1,3
The factors of 4 are 1,2,4
The factors of 5 are 1,5
The factors of 6 are 1,2,3,6
The factors of 7 are 1,7
The factors of 8 are 1,2,4,8
The factors of 9 are 1,3,9
The factors of 10 are 1,2,5,10

 

[ststern45]

Eric can you please explain this part?
7*2^1, 2^4, 3*2^3, 23*2^0, 15*2^1
I understand adding the exponents.
Thanks

 

[ststern45]

The factors of 2 are 1,2
The factors of 3 are 1,3
The factors of 4 are 1,2,4
The factors of 5 are 1,5
The factors of 6 are 1,2,3,6
The factors of 7 are 1,7
The factors of 8 are 1,2,4,8
The factors of 9 are 1,3,9
The factors of 10 are 1,2,5,10

Thanks. Factors are the numbers that can be divided into that number equally. 1 is always used.

 

[johnnyL]

Thanks. Factors are the numbers that can be divided into that number equally. 1 is always used.

Correct! 1 and the number itself.

 

[johnnyL]

Example 2:
The numbers are the following: 4 5 9 20 28
The answer is 6 according to the program calculation

2^2, 5*2^0, 9*2^0, 5*2^2, 7*2^2
2 + 0 + 0 + 2 + 2 = 6

 

[Eric W]

What program did you purchase? This seems like an extremely unusual problem.

Are you familiar with prime numbers? These are numbers that have no factors except themselves and 1. 2, 3, 5, 7, 11, 13, 17, etc. The Prime Number Theorem states that every number can be represented as a product of prime numbers in exactly 1 way. 24=2*2*2*3. 24 also equals 8*3, but that doesn't count since 8 is not prime. So to repeat your first example:

14, 16, 24, 29, 30

2*7, 2*2*2*2, 2*2*2*3, 29, 2*3*5

is the prime representation of each of those numbers. So another way to answer your question is to factor all the numbers, then count the number of 2s on the line.

* is the usual Excel symbol for multiplication. ^ is the symbol for exponentiation. So looking at 24 again, 24=2*2*2*3. But a shortcut way to say 2*2*2 is 2^3, or multiply 2 by itself 3 times. So my original answer used the exponentiation notation, and you add the exponents on the 2. The same procedure on each of your other examples yields the expected answers.

 

[johnnyL]

Example 1:
14, 16, 24, 29, 30

=

7*2^1, 2^4, 3*2^3, 23*2^0, 15*2^1

add all the exponents of 2 =
1 + 4 + 3 + 0 + 1 = 9

I think that bold part is the confusion point ... should be 29