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a few more question, please help me:---1) 2 friends were trying to find HCF of fifty distinct numbers. If they were finding the HCF of 2 numbers at a time, how many times this operation should be repeated to find the HCF of 50 numbers?
question no2). How many divisors of N=420 will be of the form 4n 1, where n is a whole number?
Question no3) How many integers N in the set of integers 1,2,3,.....100 are there such that N^2 N^3 is a perfect square?
Answers (1)
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Sol. 1.
Here, we have
Total numbers =50
firstly we have 50 numbers
Therefore we perform operation 25 times
Hence No. of times for operation performed = 49
2. Factors or divisors of 420=2x2x3x5x7
Now if it is 4n+1from the set of (3,5,7) then, we consider factors so such numbers are 15,35,21&105
all the above few numbers are of the form of either 4n+1 ie. 4n+1 or 4n-1
3. If it is N2.N3
then N2.N3=N5
=N4.N
Here, N4 is definitely a perfect square so we have to find out for 'N' only.
New 'N' can be
1,4,9,16,25,49,64,81,100