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Answers
6. 2,3,5,7,
7. 1
12. 101
13. 3780
15. 3,7
16. 12
(2) when the numbers are divided by their HCF remainder are always 0 because HCF are factors of that number and able to completely divide that number.
(4) Two prime numbers are twin prime numbers if their difference is either 2 more or 2 less than the another prime number. Example 41 and 43. Their difference is 2. There will be a gap of 2 between twin prime numbers.
(6) 210 is divisible by 2,3,5,7
(7) when we divide 97513/8 we get 1 as remainder, so if we subtract 1 from 97513 and make it 97512 then it will be divisible by 8,
97512/8 = 12189
(9) 3,4,11
3 x 4 x 11 = 132
132 - 5 = 127
127 is the number which when increased by 5 will be exactly divisible by 3 4 and 11.
(10) The largest number divides 100 and 199 and leaves 1 as remainder in each case is 99.
100/99 = 1 as remainder, as 99 x 1 = 99
199/99 = 1 as remainder, as 99 x 2 = 198
(11) If A is a multiple of B, their LCM is B a and their HCF is A.
(12) To find prime numbers we use two formulas
(6k+1) or (6k-1)
If we take k = 17
we get 6(17) -1 = 102 - 1 = 101
101 is the smallest 3 digit prime number
(13) When we divide 3778 by 9 we get 7 as remainder, so we can see that it is 2 less than 9 so if we add 2 to 3778 then we will get the number as 3780 which will be completely divisible by 9.
(15) Prime numbers whose sum is 10 are 3 and 7.
(16) Common multiple of 4 and 6 is 12.
4 = 2x2
6 = 2x3
LCM = 2x2x3 = 12.