Question 550228: in how many ways can 100 be written as the sum of two numbers,whose HCF is 1? answer choices 40,20,44,none.. Answer by JBarnum(2146) (Show Source):
You can put this solution on YOUR website! 50+50=100
hcf=50
we know they have to all be odd so 2 cant be a possible factor
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99
below i pointed out the prime numbers 9 15 21 25 27 33 35 39 45 49 51 55 57 63 65 69 75 77 81 85 87 91 93 95 99
there are 25 odd prime numbers from 1 to 100
adding the corrisponding numbers to make 100 have proven to have a few duplicates or an HCF higher than 1 as shown below:
(1) 51+49=100
hcf=1
find all the prime numbers from 1 to 100
(2) 1+99 hcf is 1
2 is prime but 2 and 98 have hcf of 2
(3) 3+97 hcf is 1
5+95 hcf is 5
(5) 7+93 hcf is 1
(6) 11+89 hcf is 1
(7) 13+87 hcf is 1
(8) 17+83 hcf is 1
(9) 19+81 hcf is 1
(10) 23+77 hcf is 1
(11) 29+71 hcf is 1
(12) 31+69 hcf is 1
(13) 37+63 hcf is 1
(14) 41+59 hcf is 1
(15) 43+57 hcf is 1
(16) 47+53 hcf is 1
______________
53+duplicate
59+duplicate
(17) 61+39 hcf is 1
(18) 67+33 hcf is 1
71+duplicate
(19) 73+27 hcf is 1
(20) 79+21 hcf is 1
83+duplicate
97+duplicate
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i count (20) different ways
if you were to flip them as in a+b to b+a if that counts as a different way then there are 40 ways
hmmm just went back over this, accidently counted the 5 thisone i made number 4 so theres only 20 or a possible 40 if numbers were reversed
(4)9+91=100
9=1 3 9
91= 1 7 13
hcf is 1
