SOLUTION: If x is the sum of all prime factors of 38, and if y is the sum of all prime factors of 84, what is the value of x-y? Please explain prime factors.

Question 52531This question is from textbook ultimate math success
: If x is the sum of all prime factors of 38, and if y is the sum of all prime factors of 84, what is the value of x-y? Please explain prime factors. This question is from textbook ultimate math success

Found 2 solutions by Earlsdon, venugopalramana:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The "Prime Factors" of a number are the factors of the number that are prime numbers. This sounds like a "circular" defintion so let's demonstrate with the numbers in your problem:
The prime factors of 38 are: 2 and 19. Why?
Well, 2 times 19 = 38 so 2 and 19 are factors of 38 (and so is 1 of course but 1 is not considered to be a prime number)
Also, 2 and 19 are "prime numbers"
What is a prime number?
A number is a prime number if it has only two factors, 1 and the number itself.
Another way of putting it is:
A number is a prime number if it can only be divided (with no remainder)
by 1 and the number itself.
Back to your problem:
The prime factors of 38 are 2 and 19
The prime factors of 84 are 2, 2, 3, and 7 (Check: 2*2*3*7 = 84)
x = 2+19 = 21
y = 2+2+3+7 = 14
x-y = 21-14 = 7
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
If x is the sum of all prime factors of 38, and if y is the sum of all prime factors of 84, what is the value of x-y? Please explain prime factors.
prime numbers are those which are not divisible by any number other than itself and 1...that is 2,3,5,7,11,13,17,19,23,29 etc...
ONE IS EXCLUDED BY CONVENTION,THOUGH IT DOES QUALIFY AS PER DEFINITION.
so if a factor is prime ,then it is called prime factors..ex..
prime facrors of 4 are 2
prime facrors of 12 are 2,3...etc....
prime factors of 38....2,19...their sum is 21=x
prime factors of 84.....2,3,7,....their sum is 12=y
x-y=21-12=9
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