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# Number Theory

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48
5
+172

Here:

May 7, 2020

#1
+1543
+3

GCD is greatest common divisor.

The divisors of 100 are,

1, 2, 4,5,10,20,25,50,100

1,2,4,5, work.

We also have the ones where we multiply something with it.

we have the ones with these numbers as factors.

3, 6,7,8 also works.

Essentially all 1-9 works since the gcd is at least 1 and at most 5.

ask if you don't understand anything.

May 7, 2020
edited by hugomimihu  May 7, 2020
edited by hugomimihu  May 7, 2020
#2
0

I count 89 such numbers as follows:

GCD of 1 and 100 = 1
GCD of 2 and 100 = 2
GCD of 3 and 100 = 1
GCD of 4 and 100 = 4
GCD of 5 and 100 = 5
GCD of 6 and 100 = 2
GCD of 7 and 100 = 1
GCD of 8 and 100 = 4
GCD of 9 and 100 = 1
GCD of 11 and 100 = 1
GCD of 12 and 100 = 4
GCD of 13 and 100 = 1
GCD of 14 and 100 = 2
GCD of 15 and 100 = 5
GCD of 16 and 100 = 4
GCD of 17 and 100 = 1
GCD of 18 and 100 = 2
GCD of 19 and 100 = 1
GCD of 21 and 100 = 1
GCD of 22 and 100 = 2
GCD of 23 and 100 = 1
GCD of 24 and 100 = 4
GCD of 26 and 100 = 2
GCD of 27 and 100 = 1
GCD of 28 and 100 = 4
GCD of 29 and 100 = 1
GCD of 31 and 100 = 1
GCD of 32 and 100 = 4
GCD of 33 and 100 = 1
GCD of 34 and 100 = 2
GCD of 35 and 100 = 5
GCD of 36 and 100 = 4
GCD of 37 and 100 = 1
GCD of 38 and 100 = 2
GCD of 39 and 100 = 1
GCD of 41 and 100 = 1
GCD of 42 and 100 = 2
GCD of 43 and 100 = 1
GCD of 44 and 100 = 4
GCD of 45 and 100 = 5
GCD of 46 and 100 = 2
GCD of 47 and 100 = 1
GCD of 48 and 100 = 4
GCD of 49 and 100 = 1
GCD of 51 and 100 = 1
GCD of 52 and 100 = 4
GCD of 53 and 100 = 1
GCD of 54 and 100 = 2
GCD of 55 and 100 = 5
GCD of 56 and 100 = 4
GCD of 57 and 100 = 1
GCD of 58 and 100 = 2
GCD of 59 and 100 = 1
GCD of 61 and 100 = 1
GCD of 62 and 100 = 2
GCD of 63 and 100 = 1
GCD of 64 and 100 = 4
GCD of 65 and 100 = 5
GCD of 66 and 100 = 2
GCD of 67 and 100 = 1
GCD of 68 and 100 = 4
GCD of 69 and 100 = 1
GCD of 71 and 100 = 1
GCD of 72 and 100 = 4
GCD of 73 and 100 = 1
GCD of 74 and 100 = 2
GCD of 76 and 100 = 4
GCD of 77 and 100 = 1
GCD of 78 and 100 = 2
GCD of 79 and 100 = 1
GCD of 81 and 100 = 1
GCD of 82 and 100 = 2
GCD of 83 and 100 = 1
GCD of 84 and 100 = 4
GCD of 85 and 100 = 5
GCD of 86 and 100 = 2
GCD of 87 and 100 = 1
GCD of 88 and 100 = 4
GCD of 89 and 100 = 1
GCD of 91 and 100 = 1
GCD of 92 and 100 = 4
GCD of 93 and 100 = 1
GCD of 94 and 100 = 2
GCD of 95 and 100 = 5
GCD of 96 and 100 = 4
GCD of 97 and 100 = 1
GCD of 98 and 100 = 2
GCD of 99 and 100 = 1

May 7, 2020
#3
+1543
+3

oh yes don't mind my earlier answer mine is incorrect sorry

May 7, 2020
#4
+172
0

Sorry but both answers are wrong! :(

May 7, 2020
#5
0

It just simple mistake in counting the above list. It appears there are only 88 such numbers.

Guest May 7, 2020