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18 Dec 2025, 07:05
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If a number n has no factor p with 1<p<n, that means the only positive divisors are 1 and n. That means n is prime (except the special case n=1 but here n>10, so n is at least 11 and prime).
q = quotient
r = remainder
Using the expression:
n=18q+r
we can deduce that, for the number n to be prime, the remainder must be relatively prime to 18 (it must not have any common factors with 18 except for 1). It also must be less than or equal to 17.
There are 6 relatively primes of 18: 1,5,7,11,13,17 which can be proven to occur with some prime>10.
The answer is D
q = quotient
r = remainder
Using the expression:
n=18q+r
we can deduce that, for the number n to be prime, the remainder must be relatively prime to 18 (it must not have any common factors with 18 except for 1). It also must be less than or equal to 17.
There are 6 relatively primes of 18: 1,5,7,11,13,17 which can be proven to occur with some prime>10.
The answer is D
18 Dec 2025, 07:15
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The correct answer is option D
The question asks us to determine the possible remainders when prime numbers greater than 10 are divided by 18. By listing some prime numbers greater than 10 and their remainders when divided by 18:-
11 -> reminder 11
13 -> reminder 13
17 -> reminder 17
19 -> reminder 1
23 -> reminder 5
43 -> reminder 7
The set of distinct reminder is ---> {1,5,7,11,13,17}
The question asks us to determine the possible remainders when prime numbers greater than 10 are divided by 18. By listing some prime numbers greater than 10 and their remainders when divided by 18:-
11 -> reminder 11
13 -> reminder 13
17 -> reminder 17
19 -> reminder 1
23 -> reminder 5
43 -> reminder 7
The set of distinct reminder is ---> {1,5,7,11,13,17}
HemanthN01
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18 Dec 2025, 07:30
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Bunuel
Ok from question we get to know that generated number has only 2 factors which means we are looking for prime numbers greater than 10 --> 11,13,17,19,23,29,31,37,41,43....
We want to find the distinct remainders we get when n/18
1) 11/18 rem=11
2) 13/18 rem=13
3) 17/18 rem=17
4) 19/18 rem=1
5) 23/18 rem=5
6) 29/18 rem=11 , 31/18 rem=13 , 37/18 rem=1, 41/18 rem=5 (all these are repeated)
7) 43/18 rem=7
So there are 6 remainders which are distinct 1,5,7,11,13,17
