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Question 762354: How many numbers less than 20 are relatively prime to 20 ?
Answer by Naveen11(1)   (Show Source):
You can put this solution on YOUR website! Solution:
The prime factorization of 20 is: 2^2 × 5^1.
Taking 2^2 first, we get: 2 - 1 = 1 and 2^(2 - 1) = 2.
Taking 5^1 we get: 5 - 1 = 4 and 5^(1-1) = 1.
Multiplying all of them together = 1 × 2 × 4 × 1 = 8.
The numbers which are relatively prime are 1 , 3 , 7 , 9 , 11 , 13 , 17 , and 19. So indeed there are 8 .
Another way of defining relatively prime number is that "Two positive integers are said to be "relatively prime" if 1 is the only number that divides both of them evenly."
All prime numbers are co-prime to each other.
Number 1 is co-prime to every integer.
Relatively prime numbers can also have only -1 as common factor.
Hence, any two integers x and y are said to be relatively prime if they have only common factor 1 or - 1.
What is a Prime Number?
A prime number is a whole number larger than the number 1 and one that can be equally divided only by itself and 1
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