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Q. How many divisors of 25200 can be expressed in the form 4n + 3, where n is a whole number?
1. 6
2. 8
3. 9
4. None of these

asked by Amit Kumar

[administration]

25200=2^4*3^2*5^2*7
so we have 2,4,8,16,3,9,5,25,7 as some factors

now a divisor can be 4n+3 only for two cases
i)when it is of the form 4n+3 and has 1 prime factor

ii)when (4n+1)(4m+3)–>4k+3 with two prime numbers

iii) when (4n+1)(4k+1)(4m+3)=4p+3 with 3 prime factors

case i)–>3,7
2 divisors

case ii)4n+1=5,9,25
so no.of divisors representible this way=3*2-1=5 divisors
3*5
3*25
7*5
7*9
7*25

case iii)4n+1—>5,9,25
we have
7*5*9 2 more cases
7*9*25
so total=2+5+2=9 divisors

 

answered by Souvik Sinha Roy

[Author]

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